Search

The aim of this research paper was to explore the various characteristics of the doubly warped product manifold, focusing particularly on aspects such as the Hessian, Riemannian curvature, Ricci curvature, and concircular curvature tensor components. By examining the necessary conditions that would classify the manifold as Riemann-flat, Ricci-flat, and concircularly-flat, the study aimed to expand our understanding of these concepts. To achieve this, the research incorporated the application of these findings to a generalized Robertson-Walker doubly warped product manifold scenario. This approach allowed us to identify and analyze the specific circumstances under which the manifold displayed concircular flatness. [ABSTRACT FROM AUTHOR]

The aim of this research paper was to explore the various characteristics of the doubly warped product manifold, focusing particularly on aspects such as the Hessian, Riemannian curvature, Ricci curvature, and concircular curvature tensor components. By examining the necessary conditions that would classify the manifold as Riemann-flat, Ricci-flat, and concircularly-flat, the study aimed to expand our understanding of these concepts. To achieve this, the research incorporated the application of these findings to a generalized Robertson-Walker doubly warped product manifold scenario. This approach allowed us to identify and analyze the specific circumstances under which the manifold displayed concircular flatness.

The object of the present paper is to study almost Kenmotsu manifolds with characteristic vector field ξ belonging to some nullity distributions, considering concircular curvature tensor. Locally concircularly symmetric almost Kenmotsu manifolds, concircularly recurrent almost Kenmotsu manifolds and locally concircularly recurrent three-dimensional almost Kenmotsu manifolds are studied. And we have obtained some interesting results. [ABSTRACT FROM AUTHOR]

Results on a concircularly semi-symmetric metric connection on a Riemannian manifold are presented. Six linearly independent curvature tensors with respect to this non-symmetric linear connection are studied, and the tensors coincident with the Weyl projective curvature tensor and the concircular curvature tensor of the Levi-Civita connection are determined. Transformations of connections when the Riemannian curvature tensor, Weyl projective curvature tensor and the concircular curvature tensor of the Levi-Civita connection are invariant are also observed. Moreover, new conditions for the Einstein manifold are derived. [ABSTRACT FROM AUTHOR]

In this present paper, a class of Lorentzian almost paracontact metric manifolds known as the LPKenmotsu (Lorentzian para-Kenmotsu) is considered that accepts a connection of quarter-symmetric. In this work, it was found that an LP-Kenmotsu manifold is either φ-symmetric or concircular φ-symmetric with respect to quarter-symmetric metric connection if and only if it is symmetric with respect to the Riemannian connection, provided the scalar curvature of Riemannian connection is constant. [ABSTRACT FROM AUTHOR]

In 1966, B. O'Neill [The fundamental equations of a submersion, Michigan Math. J., Volume 13, Issue 4 (1966), 459-469.] defined some fundamental equations and curvature rela- tions between the total space, the base space and the fibres on a submersion. In the present paper, we define new curvature tensors on Riemannian submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensor and M projective curvature tensor, respectively. Finally, we obtain some results in case of the total space of Riemannian submersions has umbilical fibres for any curvature tensors mentioned by the above. [ABSTRACT FROM AUTHOR]

The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly, (L P S) n ) to its tangent bundle T M associated with a Riemannian connection D C and a quarter-symmetric metric connection (QSMC) D ¯ C . [ABSTRACT FROM AUTHOR]

This paper studies the concircular, projective and conharmonic curvature tensors on 4-dimensional Lorentzian manifolds known as space-times. We obtain some properties of these tensor fields by relating the known holonomy algebras for Lorentz signature (+,+,+,-). For the space-times admitting special vector fields, such as parallel and recurrent vector fields, some theorems are proved. The eigenbivector structure of the investigated tensor fields is also examined in these spaces. These results obtained by considering the holonomy theory are associated with the algebraic classification of the Riemann curvature and Ricci tensors for Lorentz signature, and various examples related to the study are also given. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study and investigate the geometrical properties of a concircular curvature tensor on generalized Sasakian-space-forms. In this manner, we obtained results for ϕ-concircularly flat, ϕ-semisymmetric, locally concircularly symmetric and locally concircularly ϕ-symmetric generalized Sasakian-space-forms. Finally, we construct examples of the generalized Sasakian-space-forms to verify some results.

The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, $\xi$-projectively flat, $M$-projectively flat, $\xi$-$M$-projectively flat, pseudo projectively flat and $\xi$-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, $M$-projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily.

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with - η -Ricci solitons. First we find some necessary conditions for such a manifold to be φ -Einstein. Then, we study the notion of - η -Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study and investigate the geometrical properties of a concircular curvature tensor on generalized Sasakian-space-forms. In this manner, we obtained results for ϕ -concircularly flat, ϕ -semisymmetric, locally concircularly symmetric and locally concircularly ϕ -symmetric generalized Sasakian-space-forms. Finally, we construct examples of the generalized Sasakian-space-forms to verify some results. [ABSTRACT FROM AUTHOR]

Considering a non-symmetric linear connection and its dual one appear 6 independent curvature tensors [15]. In the present paper we study properties of curvature tensors of semi-symmetric metric connections on a generalized Riemannian manifold. It is shown that if linear connection preserves the symmetric part of the generalized Riemannian metric with semi-symmetric torsion with an appropriate additional condition, then these six curvature tensors can be expressed by linear combination of Weyl conformal curvature tensor, Weyl projective curvature tensor and the concircular curvature tensor. In the case of the curvature tensor , we have proved that if exists a linear connection preserving the symmetric part of the generalized Riemannian metric with semi-symmetric torsion, whose curvature tensor vanishes, it is necessary and sufficient that the Riemannian metric be projectively flat. For tensor we also get a useful result. If exists a linear connection preserving the symmetric part of the generalized Riemannian metric with semi-symmetric torsion, whose curvature tensor and Ricci tensor vanish, it is necessary and sufficient that the Riemannian metric be conformally flat. [ABSTRACT FROM AUTHOR]

The present paper is to deliberate the class of ϵ-Kenmotsu manifolds which admits conformal η-Ricci soliton. Here, we study some special types of Ricci tensor in connection with the conformal η-Ricci soliton of ϵ-Kenmotsu manifolds. Moving further, we investigate some curvature conditions admitting conformal η-Ricci solitons on ϵ-Kenmotsu manifolds. Next, we consider gradient conformal η-Ricci solitons and we present a characterization of the potential function. Finally, we develop an illustrative example for the existence of conformal η-Ricci soliton on ϵ-Kenmotsu manifold.

This paper reviews few curvature properties of (LCS)n-manifold endowed with torseforming vector field and concicrular curvature tensor. Moreover, we have proved several interesting results in this study. [ABSTRACT FROM AUTHOR]

In this article, the behavior of the C(α)-manifold satisfying the conditions R(X,Y)W* = 0,W* (X,Y)R = 0,W* (X,Y) Z = 0, W* (X,Y)S = 0 and W* (X,Y) C = 0 on the M--projective curvature tensor is investigated. The C(α)--Manifold is characterized according to these states of the curvature tensor. Here, W*,R,S, Z and C are M--projective, Riemann, Ricci, concircular and quasiconformal curvature tensors. [ABSTRACT FROM AUTHOR]

The present paper is an attempt to study the geometrical properties of the concircular curvature tensor on LP-Sasakian manifolds with generalised Tanaka-Webster connection. In this manner, we have shown that if an n-dimensional LP-Sasakian manifold is ξ-concircularly flat with respect to generalized Tanaka-Webster connection, then its scalar curvature with respect to generalized Tanaka-Webster connection vanishes. Also, we have proved that if an n-dimensional LP-Sasakian manifold satisfies the condition, C (X, Y). S = 0, with respect to generalized Tanaka-Webster connection, then the scalar curvature with respect to generalized Tanaka-Webster connection vanishes. [ABSTRACT FROM AUTHOR]

The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, ξ-projectively flat, M-projectively flat, ξ-M-projectively flat, pseudo projectively flat and ξ-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, M-projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily. [ABSTRACT FROM AUTHOR]

We classify Lorentzian para-Kenmotsu manifolds which satisfy the curvature conditions W2.C = 0, Z.C = LCQ(g, C), W2.Z − Z.W2 = 0 and W2.Z + Z.W2 = 0, where W2 is the Weyl- projective tensor, Z is the concircular tensor, and C is the Weyl conformal curvature tensor. We study and have shown that the manifold M is η-Einstein provided that the Weyl-projective curvature tensor W2 meets the condition W2.Z − Z.W2 = 0, and it is an Einstein manifold if W2.Z + Z.W2 = 0. Finally, in this article, we derive the conditions in relation to conformally flatness of the manifold, whenever the LP-Kenmotsu manifold satisfies the condition Z.C = LCQ(g, C). [ABSTRACT FROM AUTHOR]

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with 🟉-η-Ricci solitons. First we find some necessary conditions for such a manifold to be φ-Einstein. Then, we study the notion of 🟉-η-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results.

In this paper we study NMCP manifolds, which are (2p+2q+2)--dimensional differential manifolds with an normal metric contact pair structure. The aim of the study is to examine the Riemannian geometry of normal metric contact pair manifolds under certain conditions related to the *--Ricci tensor. We prove that a *--Ricci-semi-symmetric NMCP manifold is *--Ricci-flat, and that a *--generalized quasi-Einstein NMCP manifold cannot be *--Ricci-semi-symmetric. Finally, we consider the concircular curvature tensor on NMCP manifolds and prove that a concircular flat NMCP manifold is locally isometric to (2p+2q+2)-dimensional hyperbolic space. [ABSTRACT FROM AUTHOR]

The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.

In the present paper, we study the curvature tensors of (k;µ) - Paracontact manifold satisfying the conditions P(ξ; Y) e Z = 0, P(ξ; Y)P = 0, P(ξ; Y)S = 0 and P(ξ; Y)R = 0: According these cases, (k; μ)-Paracontact manifolds have been characterized. We obtain the necessary and sufficient conditions of a (k; µ)-Paracontact manifold to be (η-)Einsteins. [ABSTRACT FROM AUTHOR]

In the present paper, some results on a Lorentzian Sasakian manifold endowed with a quarter-symmetric metric connection have been studied.

We study a Para-Sasakian manifold admitting a type of quartersymmetric non-recurrent-metric connection whose concircular curvature tensor satisfies certain curvature conditions. [ABSTRACT FROM AUTHOR]

In this paper, anti-invariant submanifolds of a normal paracontact metric manifold are studied and characterizing the submanifold with respect to covariant derivative of the second fundamental form of anti-invariant submanifold. Furthermore, some special cases are also discussed and we give a non-trivial example which satisfies the statements of theorems. [ABSTRACT FROM AUTHOR]

The present paper deals with the study of a D-homothetic deformation of an extended generalized ϕ-recurrent (LCS)2n+1-manifolds their geometrical properties are discussed. Finally, we construct an example of an extended generalized ϕ-recurrent (LCS)3-manifolds that are neither ϕ-recurrent nor generalized ϕ-recurrent under such deformation is constructed.

In this paper, we deal with α-cosymplectic manifolds. Firstly, we give a characterization for α-cosymplectic manifold admitting a Ricci soliton given as to be η-Einstein and nearly quasi-Einstein. Also, we study yamabe solitons in α-cosymplectic manifold and obtain some important classifications about scalar curvature of this manifold. Finally, we find that if an α-cosymplectic manifold is conharmonically flat, it is an η-Einstein. [ABSTRACT FROM AUTHOR]

We characterize ∊-Kenmotsu manifolds admitting *-conformal η-Ricci solitons. At last, an example of 7-dimension ∊-Kenmotsu manifold is given. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study the properties of locally and globally Φ-concircularly symmetric Kenmotsu manifolds endowed with a semi-symmetric metric connection. First, we will prove that the locally Φ-symmetric and the globally Φ-concircularly symmetric Kenmotsu manifolds are equivalent. Next, we will study three dimensional locally Φ-symmetric, locally Φ-concircularly symmetric and locally Φ-concircularly recurrent Kenmotsu manifolds with respect to such connection and will obtain some geometrical results. In the end, we will construct a non-trivial example of Kenmotsu manifold admitting a semi-symmetric metric connection and validate our results. [ABSTRACT FROM AUTHOR]

In this paper we investigate N(k)-paracontact metric manifolds satisfying the curvature conditions R ⋅ Z = 0 and Z ⋅ S = 0, where R, Z and S are the Riemannian curvature tensor, the concircular curvature tensor and Ricci tensor, respectively. Further, we study N(k)-paracontact metric manifolds satisfying the curvature conditions Z ⋅ Z = 0 and Z ⋅ R = 0. [ABSTRACT FROM AUTHOR]

In this paper we study Kenmotsu manifold admitting a semi-symmetric metric connection whose concircular curvature tensor satisfies certain curvature conditions. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study P-Sasakian manifolds admitting a semi-symmetric non-metric connection whose concircular curvature tensor satisfies certain curvature conditions

We study the Schouten-van Kampen connection associated to a Sasakian structure. With the help of the Schouten-van Kampen connection we characterize Sasakian manifolds and find certain curvature properties of this connection on Sasakian manifolds. Also we study Ricci solitons on a Sasakian manifold with respect to the Schouten-van Kampen connection. Finally, an illustrative example is given to verify some results.

In the present paper, we have studied the curvature tensors of a normal almost paracontact metric manifold satisfying the conditions C̃(ξ,U1)R = 0, C̃(ξ,U1)P = 0, C̃(ξ,U1) Z̃ = 0, C̃(ξ,U1)S = 0 and C̃(ξ,U1)C̃= 0. According these cases, we classified normal almost paracontact metric manifolds, where R is the Riemanniann curvature tensor, C̃ is the quasi-conformal curvature tensor, Pis the projective curvature tensor, Z̃ is the concircular curvature tensor and S is the Ricci tensor. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study the concircular curvature tensor, pro jective curvature tensor, Weyl conformal curvature tensor of Kenmotsu manifolds admitting Schouten-van Kampen connection and an example is given to verify our results. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study concircularly flat Z-symmetric manifold which is a type of non-flat Riemannian manifold. In the first section, we give the definition of a concircularly flat Z-symmetric manifold. In the second section, some theorems about these manifolds are proved and some properties of them are obtained. In the last section, we give an example for the existence of this manifold. [ABSTRACT FROM AUTHOR]

The present paper deals with the study of a D-homothetic deformation of an extended generalized φ-recurrent (LCS)2n+1-manifolds their geometrical properties are discussed. Finally, we construct an example of an extended generalized φ-recurrent (LCS)3-manifolds that are neither φ-recurrent nor generalized φ-recurrent under such deformation is constructed. [ABSTRACT FROM AUTHOR]

In the present paper, we study curvature properties of η-Ricci solitons on para-Kenmotsu manifolds. We obtain some results of η-Ricci solitons on para-Kenmotsu manifolds satisfying R(ε;X):C = 0, R(ε;X):fM = 0, R(ε;X):P = 0, R(ε;X): e C = 0 and R(ε;X):H = 0, where C, fM, P, e C and H are a quasi-conformal curvature tensor, a M-projective curvature tensor, a pseudo-projective curvature tensor, and a concircular curvature tensor and conharmonic curvature tensor, respectively. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to study the Kenmotsu manifold admitting the Schouten-van Kampen connection. We study the Kenmotsu manifold admitting the Schouten-van Kampen connection satisfying certain curvature conditions. Also, we prove the equivalent conditions for the Ricci soliton in a Kenmotsu manifold to be steady with respect to the Schouten-van Kampen connection. [ABSTRACT FROM AUTHOR]

Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on MS(QE)4 for both the Riemannian and Lorentzian cases.

The aim of this work is to examine some properties of the concircular curvature tensor on 4--dimensional manifolds admitting a Lorentz metric (so called space-times). In the first two sections, the study is introduced and the interrelated concepts together with some notations are presented. In the third section of the study, some results are obtained connected to eigenbivector structure of the concircular curvature tensor on these manifolds by taking into account the classification scheme of 2-forms (also known as bivectors) in this metric signature. Then, the known holonomy algebras on space-times are considered and some theorems are given regarding the concircular and Riemann curvature tensors. This analysis is also associated with the types of the Riemann curvature tensor on these manifolds. In the last section, the results of the study is summarized and the discussion part is presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the Weyl conformal curvature tensor W and the concircular curvature tensor C on a (k, μ)'-almost Kenmotsu manifold M2n+1 of dimension greater than 3. We obtain that if M2n+1 satisfies either R. W = 0 or C . C = 0, then it is locally isometric to either the hyperbolic space H2n+1(-1) or the Riemannian product Hn+1(-4)×Rn [ABSTRACT FROM AUTHOR]

The object of the present paper is to study a Para-Sasakian manifold admitting a type of quarter-symmetric metric connection whose concircular curvature tensor satisfies certain curvature conditions. [ABSTRACT FROM AUTHOR]

In this paper, a new type of generalized quasi-Einstein manifold is defined. The special cases of this manifold are Einstein manifold, quasi-Einstein manifold and nearly quasi-Einstein manifold. We have shown the existence of this new type of generalised quasi-Einstein manifold by a suitable example. [ABSTRACT FROM AUTHOR]