On submanifolds of Sasakian statistical manifolds

‎In this paper‎, ‎invariant and‎ ‎anti-invariant submanifolds of Sasakian statistical manifolds are studied‎. ‎Necessary and sufficient conditions are given for vanishing the dual connection in the normal bundle‎. ‎Moreover‎, ‎existence of a Kaehlerian structure on invariant hypersurfaces of Sasakian statistical manifolds are proved‎.

Types of Submanifolds in Metallic Riemannian Manifolds: A Short Survey

We provide a brief survey on the properties of submanifolds in metallic Riemannian manifolds. We focus on slant, semi-slant and hemi-slant submanifolds in metallic Riemannian manifolds and, in particular, on invariant, anti-invariant and semi-invariant submanifolds. We also describe the warped product bi-slant and, in particular, warped product semi-slant and warped product hemi-slant submanifolds in locally metallic Riemannian manifolds, obtaining some results regarding the existence and nonexistence of non-trivial semi-invariant, semi-slant and hemi-slant warped product submanifolds. We illustrate all these by suitable examples.

Certain results on invariant submanifolds of an almost Kenmotsu $$(\kappa ,\mu ,\nu )$$-space

In the present paper, we study invariant submanifolds of almost Kenmotsu structures whose Riemannian curvature tensor has $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -nullity distribution. Since the geometry of an invariant submanifold inherits almost all properties of the ambient manifold, we research how the functions $$\kappa ,\mu $$ κ , μ and $$\nu $$ ν behave on the submanifold. In this connection, necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -space to be totally geodesic under some conditions.

Study of Differential Equations on Warped Product Semi-Invariant Submanifolds of the Generalized Sasakian Space Forms

The purpose of the present paper is to study the applications of Ricci curvature inequalities of warped product semi-invariant product submanifolds in terms of some differential equations. More precisely, by analyzing Bochner’s formula on these inequalities, we demonstrate that, under certain conditions, the base of these submanifolds is isometric to Euclidean space. We also look at the effects of certain differential equations on warped product semi-invariant product submanifolds and show that the base is isometric to a special type of warped product under some geometric conditions.

Invariant Pseudoparallel Submanifolds of an Almost $\alpha$-Cosymplectic $(\kappa,\mu,\nu)$-Space

In this article, the geometry of pseudoparallel, Ricci-generalized pseudoparallel and 2-Ricci-generalized pseudoparallel invariant submanifolds of an almost $\alpha$-cosymplectic $(\kappa,\mu,\nu)$ space has been searched under the some conditions. We also give some characterizations for such submanifolds. I think that obtained new results contribute to differential geometry.

ON f-KENMOTSU MANIFOLDS AND THEIR SUBMANIFOLDS WITH QUARTER SYMMETRIC METRIC CONNECTIONS

The object of the present paper is to study invariant submanifolds of f-Kenmotsu manifolds with respect to quarter symmetric metric connections. Some necessary and sufficient conditions for such submanifolds to be totally geodesic have been deduced. Also we construct an example of a submanifold of a five-dimensional f-Kenmotsu manifold to justify our results.

On invariant submanifolds of paracompact (k;m)-spaces

The object of the present paper is to deduce some necessary and sufficient conditions for invariant Submanifolds of paracontact (κ, µ)-spaces to be totally geodesic. We also establish that a totally umbilical invariant submanifold of a paracontact (κ, µ)-manifold is also totally geodesic. Some more necessary and sufficient conditions for a submanifold of a paracontact (κ, µ)-manifold to be totally geodesic have been deduced using parallelity and pseudo parallelity of the second fundamental form. In the last section we obtain some results on paracontact (κ, µ)-manifold with concircular canonical field.