Search

This work investigates the effects on the factor manifolds of a singly warped product manifold resulting from the presence of a quasi-conformally flat, quasi-conformally symmetric, or divergence-free quasi-conformal curvature tensor. Quasi-conformally flat warped product manifolds exhibit three distinct scenarios: in one scenario, the base manifold has a constant curvature, while in the other two scenarios, it is quasi-Einstein. Alternatively, the fiber manifold has a constant curvature in two scenarios and is Einstein in one scenario. Quasi-conformally symmetric warped product manifolds present three distinct cases: in the first scenario, the base manifold is Ricci-symmetric and the fiber is Einstein; in the second case, the base manifold is Cartan-symmetric and the fiber has constant curvature; and in the last case, the fiber is Cartan-symmetric, and the Ricci tensor of the base manifold is of Codazzi type. Finally, conditions are provided for singly warped product manifolds that admit a divergence-free quasi-conformal curvature tensor to ensure that the Riemann curvature tensors of the factor manifolds are harmonic. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel curvature tensor called the 풦-curvature tensor, which is formed by combining the Weyl tensor and the 풲2-curvature tensor. It is proved that a semi-Riemannian manifold with traceless 풦-curvature tensor is Einstein, while a 풦-curvature flat semi-Riemannian manifold exhibits constant sectional curvature. We show that a space-time with traceless 풦-curvature tensor or 풦-curvature flat represents dark energy era. A semi-Riemannian manifold with divergence-free 풦-curvature tensor is Weyl harmonic. In a space-time where the 풦-curvature tensor is of divergence-free, both the isotropic pressure and energy density are constants. Under certain conditions, it is shown that a pseudo-풦-symmetric semi-Riemannian manifold reduces to a pseudo-Riemannian manifold. It is demonstrated that pseudo-풦-symmetric space-times can be regarded as generalized Robertson–Walker (GRW) space-times. Finally, a concrete example of pseudo-풦-symmetric semi-Riemannian manifolds is presented. [ABSTRACT FROM AUTHOR]

This paper investigates singly warped product manifolds admitting semi-conformal curvature tensors. The form of the Riemann tensor and Ricci tensor of the base and fiber manifolds of a semi-conformally flat singly warped product manifold are provided. It is demonstrated that the fiber manifold of a semi-conformally flat warped product manifold has a constant curvature. Sufficient requirements on the warping function to ensure that the base manifold is a quasi-Einstein or an Einstein manifold are provided. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the η -Einstein cosymplectic manifolds with the gradient Einstein solitons and the conformal vector fields. It is proven that if an η -Einstein cosymplectic manifold M 2 n + 1 of dimension 2 n + 1 with n > 1 admits a gradient Einstein soliton, then either M 2 n + 1 is Ricci flat or the gradient of Einstein potential function is pointwise collinear with the Reeb vector field of M 2 n + 1 . Also, we prove that if M 2 n + 1 admits a conformal vector field W , then either M 2 n + 1 is Ricci flat or W is homothetic. We also establish that a conformal vector field W on M 2 n + 1 is a strict infinitesimal contact transformation, provided the scalar curvature of M 2 n + 1 is constant. Finally, the non-trivial examples of cosymplectic manifolds admitting the gradient Einstein solitons are given. [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize almost co-Kähler manifolds and co-Kähler three-manifolds whose metrices are the gradient ρ -Einstein solitons. At first we prove that a proper (κ ̃ , μ ̃) -almost co-Kähler manifold with κ ̃ < 0 does not admit gradient ρ -Einstein soliton. It is also shown that if a proper -Einstein almost co-Kähler manifold with constant coefficients admits a gradient ρ -Einstein soliton, then either the manifold is a K -almost co-Kähler manifold or the soliton is trivial. Next, we prove that in case of co-Kähler three-manifold the manifold is of constant scalar curvature. Moreover, either the manifold is flat or the gradient of the potential function is collinear with the Reeb vector field ξ. Finally, we construct two examples to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, Yamabe solitons, gradient Yamabe solitons and gradient ρ -Einstein solitons have been investigated on 3-dimensional f -Kenmotsu manifolds. Moreover, we characterize 3-dimensional f -Kenmotsu manifolds admitting *-Ricci solitons and gradient *-Ricci solitons, respectively. [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric. [ABSTRACT FROM AUTHOR]

In this paper, warped product mixed generalized quasi-Einstein manifolds MG(QE) n are studied. It is shown that a Ricci recurrent MG(QE) n manifold is a product manifold whose factors are Ricci recurrent. Sufficient conditions for a MG(QE) n to be a G(QE) n are derived. Then, we classify three types of warped product MG(QE) n . For example, it is proved that the fiber manifold is Einstein in the first type, (QE) n in the second type and MG(QE) n in the third type. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mathematical Physics, Analysis, Geometry (18129471) is the property of B Verkin Institute for Low Temperature Physics & Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The purpose of the offering exposition is to characterize gradient Yamabe, gradient Einstein and gradient m -quasi Einstein solitons within the framework of 3-dimensional para-Kenmotsu manifolds. Finally, we consider an example to prove the result obtained in previous section. [ABSTRACT FROM AUTHOR]

We characterize almost co-Kähler manifolds with gradient Yamabe, gradient Einstein and quasi-Yamabe solitons. It is proved that if the metric of a (κ , μ) -almost co-Kähler manifold M 2 n + 1 is a gradient Yamabe soliton, then M 2 n + 1 is either K -almost co-Kähler or N (κ) -almost co-Kähler or the metric of M 2 n + 1 is a trivial gradient Yamabe soliton. A (κ , μ) -almost co-Kähler manifold with gradient Einstein soliton is K -almost co-Kähler. Finally, it is shown that an almost co-Kähler manifold admitting a quasi-Yamabe soliton, whose soliton vector is pointwise collinear with the Reeb vector field of the manifold, is K -almost co-Kähler. Consequently, some results of almost co-Kähler manifolds are deduced. [ABSTRACT FROM AUTHOR]

Recently, it is proven that generalized Robertson–Walker space-times in all orthogonal subspaces of Gray's decomposition except one (unrestricted) are perfect fluid space-times. GRW space-times in the unrestricted subspace are identified by having constant scalar curvature. Generalized quasi-Einstein GRW space-times have a constant scalar curvature. It is shown that generalized quasi-Einstein GRW space-times reduce to Einstein space-times or perfect fluid space-times. [ABSTRACT FROM AUTHOR]

The object of this paper is to classify paracontact metric (κ; _≢)-spaces satisfying certain curvature conditions. We show that a paracontact metric (κ; _≢)-space is Ricci semisymmetric if and only if the metric is Einstein, provided κ < -1. Also we prove that a paracontact metric (κ _≢)-space is ϕ-Ricci symmetric if and only if the metric is Einstein, provided κ ≢= 0-1. Moreover, we show that in a paracontact metric (κ _≢)-space with κ < -1, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor. Several consequences of these results are discussed. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study almost pseudo-Q-symmetric manifolds A(PQS)n. Some geometric properties have been studied which recover some known results of pseudo Q-symmetric manifolds. We obtain a necessary and sufficient condition for the 𝒬-curvature tensor to be recurrent in A(PQS)n. Also, we provide several interesting results. Among others, we prove that a Ricci symmetric A(PQS)n is an Einstein manifold under certain condition. Moreover we deal with 𝒬-flat perfect fluid, dust fluid and radiation era perfect fluid spacetimes respectively. As a consequence, we obtain some important results. Finally, we consider A(PQS)4-spacetimes. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study N(k)-quasi-Einstein manifolds. study We an N(k)-quasi-Einstein manifold satisfying the curvature conditions R(ξ,X)· Z = 0, Z(X, ·) · R = 0, and P(·,X) · Z = 0, where R, P and Z denote the Riemannian curvature tensor, the projective curvature tensor and Z tensor respectively. Next we prove that the curvature condition C · Z = 0 holds in an N(k)-quasi-Einstein manifold, where C is the conformal curvature tensor. We also study Z-recurrent N(k)-quasi-Einstein manifolds. Finally, we construct an example of an N(k)-quasi-Einstein manifold and mention some physical examples. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study a type of Riemannian manifold called generalized quasi-Einstein manifold. The existence of a generalized quasi-Einstein manifold have been proved by non-trivial examples. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study Kenmotsu manifolds admitting a W2-curvature tensor. [ABSTRACT FROM AUTHOR]

The object of the present paper is to introduce and investigate the P -curvature tensor that generalizes projective, conharmonic, M -projective and the set of W i curvature tensors introduced by Pokhariyal and Mishra. It is proven that pseudo-Riemannian manifolds admitting a traceless P -curvature tensor are Einstein and those admitting flat P -curvature tensor has a constant curvature. Classification theorems for pseudo-Riemannian manifolds admitting a divergence-free P -curvature tensor are given in each subspace of Gray's decomposition of the covariant derivative of the Ricci tensor. Space–times having a flat P -curvature tensor or a divergence free P -curvature tensor are scrutinized. Finally, perfect fluid space–times admitting various features of the P -curvature tensor are considered. [ABSTRACT FROM AUTHOR]

The object of the present paper is to characterize spacetimes with different types of energy–momentum tensor. At first we consider spacetimes with pseudo symmetric energy–momentum tensor T. We obtain a necessary and sufficient condition for a spacetime with pseudo symmetric energy–momentum tensor to be a pseudo Ricci symmetric spacetime. Next we consider the spacetimes with Codazzi type of energy–momentum tensor and several interesting results are pointed out. Moreover, some results related to perfect fluid spacetimes with different forms of energy–momentum tensors have been obtained. We study spacetimes with quadratic Killing energy–momentum tensor T and show that a GRW spacetime with quadratic Killing energy–momentum tensor is an Einstein space. Finally, we have considered general relativistic spacetimes with semisymmetric energy–momentum tensor and obtained some important results. [ABSTRACT FROM AUTHOR]