On submanifolds of Sasakian manifolds

Proceedings of the Estonian Academy of Sciences, 2012

The object of the present paper is to find necessary and sufficient conditions for invariant submanifolds of trans-Sasakian manifolds to be totally geodesic. As a remark, particular cases of submanifolds of α-Sasakian and β-Kenmotsu manifolds are considered and the difference between the conditions for submanifolds of α-Sasakian and β-Kenmotsu manifolds to be totally geodesic is shown.

2021

In this paper, we consider invariant submanifolds of an ( )-Sasakian manifolds. We show that if the second fundamental form of an invariant submanifold of a ( )-Sasakian manifold is recurrent then the submanifold is totally geodesic. We also prove that, invariant submanifolds of an Einstein ( )-Sasakian manifolds satisfying the conditions C̃(X,Y ) · σ = 0 and C̃(X,Y ) · ∇̃σ = 0 with r 6= n(n− 1) are also totally geodesic. 2010 Mathematics Subject Classification. 53C25, 53C40, 53C50, 53D10.

2017

The object of this paper is to obtain some necessary and sufficient conditions for an invariant submanifold of a LPSasakian manifold to be totally geodesic.We consider the pseudo projective and Quasi conformal invariant submanifolds of Lorentzian para-sasakian manifolds.

2010

In this paper, invariant submanifolds of a trans-Sasakian manifold are studied. Necessary and sufficient conditions are given on a submanifold of a trans-Sasakian manifold to be invariant submanifold.In this case, we investigate further properties of invariant submanifolds of a transSasakian manifold. An addition, some theorems are given related to an invariant submanifold of a trans-Sasakian manifold. M.S.C. 2000: 53C17, 53C25, 53C40.

2012

A structure on an almost contact metric manifold is defined as a generalization of well-known cases: Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic. This was suggested by a local formula of Eum [9]. Then we consider a semi-invariant ξ⊥-submanifold of a manifold endowed with such a structure and two topics are studied: the integrability of distributions defined by this submanifold and characterizations for the totally umbilical case. In particular we recover results of Kenmotsu [11], Eum [9, 10] and Papaghiuc [16]. 1. Preliminaries and basic formulae An interesting topic in the differential geometry is the theory of submanifolds in spaces endowed with additional structures, see [7]. In 1978, A. Bejancu (in [2]) studied CR-submanifolds in Kähler manifolds. Starting from it, several papers have been appeared in this field. Let us mention only few of them: a series of papers of B.Y. Chen (e.g. [6]), of A. Bejancu and N. Papaghiuc (e.g. [3] in which the authors studied semi-invarian...

Turkish Journal of Analysis and Number Theory, 2020

The object of the present paper is to study invariant pseudo parallel submanifolds of a LP-Sasakian manifold and obtain the conditions under which the submanifolds are pseudoparallel, 2-pseudoparallel, generalized pseudoparallel and 2-generalized pseduoparallel. Finally, a non-trivial example is used to demonstrate that the method presented in this paper is effective.

JP Journal of Geometry and Topology, 2016

Studying in submanifolds of para-Sasakian manifolds, we obtain that (1) semi-parallel and 2-semi-parallel invariant submanifolds are totally geodesic, (2) necessary and sufficient conditions for the integrability of distributions and (3) some characterizations for submanifolds to be semi-invariant.

Filomat

In this paper, we study the geometry of the pseudo-slant submanifolds of a Sasakian space form. Necessary and sufficient conditions are given for a submanifold to be pseudo-slant submanifolds, pseudo-slant product, mixed geodesic and totally geodesic in Sasakian manifolds. Finally, we give some results for totally umbilical pseudo-slant submanifolds of Sasakian manifolds and Sasakian space forms.

2011

ABSTRACT In this paper we prove some inequalities, relating the scalar curvature R and the mean curvature vector field H of an anti-invariant submanifold in a generalized Sasakian space form M ¯(f 1 ,f 2 ,f 3 ). Also, we obtain a necessary condition for such anti-invariant submanifolds to admit a minimal manifold.

International Journal of Mathematics and …, 2010

We study warped product Pseudo-slant submanifolds of Sasakian manifolds. We prove a theorem for the existence of warped product submanifolds of a Sasakian manifold in terms of the canonical structure F.