On invariant submanifolds of trans-Sasakian manifolds (original) (raw)

Invariant submanifolds of trans-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.

A Note on Invariant Submanifolds of LP-Sasakian Manifolds

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.

On submanifolds of Sasakian manifolds

Lobachevskii Journal of Mathematics, 2011

The object of the present paper is to introduce a new type of invariant submanifolds, namely, mixed-invariant submanifolds of Sasakian manifolds and to show that everymixed-invariant submanifold of a Sasakian manifold is totally geodesic. 2-quasi-umbilical hypersurface of a Sasakian space form is also studied.

Invariant Submanifolds of ( )-Sasakian Manifolds

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.

On Submanifolds of Para-Sasakian Manifolds

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.

Some Classes of Invariant Submanifolds of LP-Sasakian Manifolds

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.

On Semi-invariant submanifolds of Nearly trans-Sasakian manifolds

Int. J. Pure & Appl. Math. Sci. Vol, 2004

Semi-invariant submanifolds of a nearly trans-Sasakian manifold are studied. Nijenhuis tensor in a nearly trans-Sasakian manifold is calculated. Integra-bility conditions for some distributions on a semi-invariant submanifold of a nearly trans-Sasakian manifold are investigated. ...

Semi-Invariant Ξ⊥-Submanifolds of Generalized Quasi-Sasakian Manifolds

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...

On Semi-Invariant Submanifolds of Trans-Sasakian Finsler Manifolds

Fundamental Journal of Mathematics and Applications, 2018

We define trans-Sasakian Finsler manifold barF2n+1=(mathcalbarN,mathcalbarNprime,barF)\bar{F}^{2n+1}=(\mathcal{\bar{N}}, \mathcal{\bar{N^{\prime }}}, \bar{F})barF2n+1=(mathcalbarN,mathcalbarNprime,barF) and semi-invariant submanifold Fm=(mathcalN,mathcalNprime,F)F^{m}=(\mathcal{N}, \mathcal {N^{\prime }}, F)Fm=(mathcalN,mathcalNprime,F) of a trans-Sasakian Finsler manifold barF2n+1\bar{F}^{2n+1}barF2n+1. Then we study mixed totally geodesic and totally umbilical semi-invariant submanifolds of trans Sasakian Finsler manifold.

Some results for anti-invariant submanifold in generalized Sasakian space form

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.