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The purpose of this paper is to investigate a warped product of hemi-slant submanifolds on an S-manifold. We prove many interesting results for the existence of warped product hemi-slant submanifold of the type M θ × f M ⊥ with ξ α ∈ M θ of an S-manifold. For such submanifolds, a characterization theorem is proven. In addition, we form an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. We also provide some examples, and the equality case is also considered. [ABSTRACT FROM AUTHOR]

The present paper aims to study pseudo-slant submanifolds of an r-Sasakian manifold and find few results. The integrability conditions of distributions that involve in the definition of pseudo-slant submanifolds of an r-Sasakian manifold are investigated. Finally, the necessary & sufficient condition for a pseudo-slant submanifold of an r-Sasakian manifold to be the pseudo-slant product is obtained successfully. [ABSTRACT FROM AUTHOR]

In this article, we study sequential warped product submanifolds of Sasakian manifolds and provide nonexistence results when the sequential warped product contains one invariant, one pointwise slant and one anti-invariant submanifold. For the only two possible types, we deduce some properties and establish Chen’s inequality in these cases. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to introduce new class of Riemannian maps which are called pointwise slant Riemannian maps (briefly, PSRM ) as a natural generalization of pointwise slant submanifolds which were introduced by Chen and Garay (Turkish J Math 36:630–640, 2012) and pointwise slant submersions which were defined by Lee and Şahin (Bull Korean Math Soc 51(4):1115–1126, 2014]. We mention many examples and investigate the geometry of foliations which are arisen from the definition of a PSRM and obtain decomposition theorems using the existence of PSRM . Moreover, we find necessary and sufficient conditions for PSRM to be totally geodesic and investigate the harmonicity of such maps. Finally, we get two inequalities in terms of the second fundamental form of a PSRM and check the equality case. [ABSTRACT FROM AUTHOR]

In this paper, we study the biwarped product submanifold in locally nearly metallic Riemannian manifold. We construct a non trivial example of a biwarped product submanifold in metallic Riemannian manifold. Moreover, we discuss a necessary and sufficient condition for such submanifolds to be locally trivial. Finally, we set up an inequality in locally nearly metallic Riemannian manifold for the second fundamental form with respect to some conditions. We also investigate the equality case. [ABSTRACT FROM AUTHOR]

In this paper, we study slant submanifolds of a para-Kenmotsu manifold. We prove that totally umbilical slant submanifold of a para-Kenmotsu manifold is either invariant or anti-invariant or dimension of submanifold is 1 or the mean curvature vector H of the submanifold lies in the invariant normal subbundle.

In this paper, slant submanifolds of a pseudo-Riemannian manifold equipped with an almost paracontact structure are defined and studied. Some characterization theorems for slant submanifolds are obtained. We also present some examples of slant submanifolds when the ambient space is an almost paracontact metric manifold. [ABSTRACT FROM AUTHOR]

In this paper, we prove that there are no non-trivial PR-semi-slant warped product submanifolds with proper slant coefficients in para-Kahler manifolds M. We also present a numerical example that illustrates the existence of a PR-warped product submanifold in M. [ABSTRACT FROM AUTHOR]

We study bi-warped product submanifolds of nearly Kaehler manifolds which are the natural extension of warped products. We prove that every bi-warped product submanifold of the form M = M T × f 1 M ⊥ × f 2 M θ in a nearly Kaehler manifold satisfies the following sharp inequality: ‖ h ‖ 2 ≥ 2 p ‖ ∇ (ln f 1) ‖ 2 + 4 q 1 + 10 9 cot 2 θ ‖ ∇ (ln f 2) ‖ 2 , where p = dim M ⊥ , q = 1 2 dim M θ , and f 1 , f 2 are smooth positive functions on M T . We also investigate the equality case of this inequality. Further, some applications of this inequality are also given. [ABSTRACT FROM AUTHOR]

In this paper, we study the geometry of the contact pseudo-slant submanifolds of an (ε)--para Sasakian space form. We give some results for totally umbilical pseudo-slant submanifolds of an (ε)--para Sasakian manifolds and an (ε)--para Sasakian space forms. It is proved that such manifolds are η-Einstein. Finally, we have verified the theorems by providing an example of 5- dimensional proper contact pseudo-slant submanifold of ℝ9 with it's usual almost paracontact metric structure. [ABSTRACT FROM AUTHOR]

The present article deals with the study of PR-pseudo-slant warped product submanifolds of paracosymplectic manifols MÌ…. Results of non-existence for non-trivial PR-pseudo-slant warped product submanifolds with proper slant coefficient in MÌ… are shown. In addition to these results, we give an elementary illustration of non-trivial PR-pseudo-slant warped product submanifold with improper slant coefficient in MÌ…. [ABSTRACT FROM AUTHOR]

In this paper, we study pseudo-slant submanifolds of a Sasakian manifold. We find some results and investigate the integrability conditions of distributions which are involved in the definition of pseudo-slant submanifolds. Finally, we obtain the necessary and sufficient condition for a pseudo-slant submanifold to be pseudo-slant product. [ABSTRACT FROM AUTHOR]

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In the present note we have derived some basic results pertaining to the geometry of slant and hemislant submanifolds of an (∊)-para Sasakian manifold. In particular, we have obtained few results on a totally umbilical slant submanifold of an (∊)-para Sasakian manifold. In the next section, we have obtained the integrability conditions of the involved distributions of hemislant submanifold of an (∊)-para Sasakian manifold. Finally we have verified the theorems by providing an example of three dimensional hemislant submanifold of (∊)-para Sasakian manifold. [ABSTRACT FROM AUTHOR]

In this paper we define slant submanifolds in neutral almost contact pseudo-metric manifolds, with motivations and examples. We also provide some natural examples of the ambient spaces. [ABSTRACT FROM AUTHOR]

In this paper, we study the geometry of slant submanifolds of conformal (k, μ)- contact manifold when the tensor field Q is parallel. Further, we give a necessary and sufficient condition for a 3-dimensional slant submanifold of a 5-dimensional conformal (k, μ)- contact manifold to be a proper slant submanifold. [ABSTRACT FROM AUTHOR]

Non-existence of warped product semi-slant submanifolds of Kaehler manifolds was proved in Sahin (Geom Dedic 117:195-202, 2006), it is interesting to find their existence in a more general setting, e.g., nearly Kaehler manifolds. In this paper, we obtain a necessary and sufficient condition for a semi-slant submanifold of a nearly Kaehler manifold to be a locally warped product. Also, we establish an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. Furthermore, the equality case of the statement is also considered. [ABSTRACT FROM AUTHOR]

In this paper, we prove an inequality between the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for slant submanifolds of generalized complex space form. Moreover, we characterize those submanifolds for which the equality case holds. [ABSTRACT FROM AUTHOR]

In this paper, conditions for K-contact, Sasakian, and cosymplectic structures to be invariant under gauge transformation are found. Moreover, the same question is studied for 3-Sasakian, 3-almost contact, and 3-cosymplectic manifolds. Finally, it is shown that a slant submanifold of an almost contact metric manifold is invariant by gauge transformation. [ABSTRACT FROM AUTHOR]

In this paper, we have studied the smallest dimensional submanifold of para β-Kenmotsu manifold. Necessary and sufficient conditions are given on 3-dimensional submanifolds of a 5-dimensional para β-Kenmotsu manifold to be a slant submanifold. After that, we have studied the 3-dimensional minimal slant submanifolds of para β- Kenmotsu manifold. [ABSTRACT FROM AUTHOR]

In this paper, we study slant submanifolds of (k, u)-contact manifold and obtain some results. We also give a necessary and sufficient condition for three dimensional submanifold of five dimensional (k, u)- contact manifold to be a minimal proper slant submanifold. [ABSTRACT FROM AUTHOR]

In this paper we give a new proof for two sharp inequalities involving generalized normalized δ-Casorati curvatures of a slant submanifold in a quaternionic space form. These inequalities were recently obtained in Lee and Vîlcu (Taiwan. J. Math. 19(3):691-702, 2015) using an optimization procedure by showing that a quadratic polynomial in the components of the second fundamental form is parabolic. The new proof is obtained analyzing a suitable constrained extremum problem on submanifold. [ABSTRACT FROM AUTHOR]

Warped product submanifolds of nearly cosymplectic manifolds were studied in Uddin et al. (Math. Probl. Eng. 2011, doi:), Uddin and Khan (J. Inequal. Appl. 2012:304, 2012) and Uddin et al. (Rev. Unión Mat. Argent. 55:55-69, 2014). In this paper, we study warped product submanifolds of nearly cosymplectic manifolds in which the base manifold is slant and thus we derive a sharp relation for the squared norm of the second fundamental form. The equality case is also considered. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we study totally umbilical proper slant submanifolds of a nearly Kaehler manifold. We prove that every totally umbilical proper slant submanifold of a nearly Kaehler manifold is totally geodesic.

In this article, we study slant and semi-slant submanifolds of (LCS)n-manifolds. Integrability conditions of distributions involved in definition of semi-slant submanifolds of a (LCS)n-manifold have been obtained. [ABSTRACT FROM AUTHOR]

Abstract: The normal scalar curvature conjecture, also known as the DDVV conjecture, was formulated by De Smet et al. (1999). It was proven recently by Lu (2011) and by Ge and Tang (2008) independently. We obtain the DDVV inequality, also known as the generalized Wintgen inequality, for Lagrangian submanifolds in complex space forms. Some applications are given. Also we state such an inequality for slant submanifolds in complex space forms. [Copyright &y& Elsevier]

In this study, we search slant submanifolds of almost product semi-Riemannian manifold. Accordingly, we investigate slant submanifolds of semi-Riemannian manifold by making the classifications as slant Riemannian, slant semi-Riemannian and slant lightlike submanifold. Moreover, we add the theorems which characterize existence of slant submanifold. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of slant submanifold of an almost contact metric 3-structure manifold. We give some examples and characterize these submanifolds. Moreover, Sasakian slant submanifolds of an almost contact 3-structure manifold are defined and studied. We also establish a sharp inequality including the squared mean curvature and Ricci curvature of a Sasakian slant submanifold. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study slant submanifolds of an N(k)-contact metric manifold. We study the parallelism of Q, and find out necessary and sufficient conditions for the existence of proper slant submanifolds of N(k)-contact metric manifolds. [ABSTRACT FROM AUTHOR]

We show new results on when a pseudo-slant submanifold is a LCS-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudoslant product and give necessary and sufficient conditions for a pseudo-slant submanifold to be the pseudo-slant product. Also we give an example of a slant submanifold in an LCS-manifold to illustrate the subject. [ABSTRACT FROM AUTHOR]

In the present paper, we study warped product semi-slant submanifolds of a Kenmotsu manifold. We obtain some results on the existence of such type warped product submanifolds of a Kenmotsu manifold with an example. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study Chen inequalities for slant, bi-slant and semi-slant submanifolds in generalized complex space forms. [ABSTRACT FROM AUTHOR]

In this paper some B.-Y. Chen inequalities for slant submanifolds in quaternionic space forms are established. [ABSTRACT FROM AUTHOR]

In this paper, we prove that there do not exist contact totally umbilical proper slant submanifolds of cosymplectic manifolds. [ABSTRACT FROM AUTHOR]

In the present paper, we study warped product semi-slant submanifolds of trans-Sasakian manifolds. We have obtained results on the existence of warped product semi-slant submanifolds of trans-Sasakian manifolds in term of the canonical structure F. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to study slant submanifolds in the setting of LP-contact manifolds. In particular, we have studied the slant submanifolds of an LP-Sasakian manifold via some curvature tensors. [ABSTRACT FROM AUTHOR]

We study non-anti-invariant slant submanifolds of generalized S-space-forms with two structure vector felds in order to know if they inherit the ambient structure. In this context, we focus on totally geodesic, totally umbilical, totally ƒ-geodesic and totally ƒ-umbilical non-anti-invariant slant submanifolds and obtain some obstructions. Moreover, we present some new interesting examples of generalized S-space-forms. [ABSTRACT FROM AUTHOR]

We establish an interesting link between differential geometry and graph theory by defining submanifolds weakly associated with graphs.We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low dimensions or belonging to some special families. [ABSTRACT FROM AUTHOR]

We give an intrinsic characterization of slant submanifolds of a Kenmotsu manifold in terms of the induced metric and show that a slant submanifold of a Kenmotsu manifold is a Kenmotsu manifold. We also prove a theorem to obtain examples of slant submanifolds of Kenmotsu manifold. [ABSTRACT FROM AUTHOR]

In this paper, we study slant submanifolds of a Kaehler product manifold. We show that an F-invariant slant submanifold of Kaehler product manifold is a product manifold. We also obtain some curvature inequalities in terms of scalar curvature and Ricci tensor. [ABSTRACT FROM AUTHOR]

In this article, we establish inequalities between the Ricci curvature and the squared mean curvature, and also between the κ-Ricci curvature and the scalar curvature for a slant, semi-slant and bi-slant submanifold in a cosymplectic space form of constant φ- sectional curvature with arbitrary codimension. [ABSTRACT FROM AUTHOR]

In the present paper, we establish Chen inequalities for slant submanifolds in Sasakian space forms, by using subspaces orthogonal to the Reeb vector field ξ. [ABSTRACT FROM AUTHOR]

We define and study both bi-slant and semi-slant submanifolds of an almost contact metric manifold and, in particular, of a Sasakian manifold. We prove a characterization theorem for semi-slant submanifolds and we obtain integrability conditions for the distributions which are involved in the definition of such submanifolds. We also study an interesting particular class of semi-slant submanifolds. [ABSTRACT FROM AUTHOR]