On Semi-invariant submanifolds of Nearly trans-Sasakian manifolds

Semi-invariant submanifold of a trans Sasakian manifold has been studies. In the present paper we study semi invariant submanifolds of a nearly trans hyperbolic Sasakian manifold. Nejenhuis tensor in a nearly trans hyperbolic Sasakian manifold is calculated. Integrability conditions for some distributions on a semi invariant submanifold of a nearly trans hyperbolic Sasakian manifold are investigated.

2013

We define a semi-symmetric semi-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a semi-symmetric semi-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

International Journal of Contemporary Mathematical Sciences, 2014

We define a quarter symmetric non-metric connection in a nearly Sasakian manifold and we study semi-invariant submanifolds of a nearly Sasakian manifold endowed with a quarter symmetric non-metric connection. Moreover, we discuss the integrability of distributions on semiinvariant submanifolds.

Journal of Applied Mathematics and Physics, 2014

This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric nonmetric connection are discussed.

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...

Journal of Applied Mathematics and Physics, 2014

This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric nonmetric connection are discussed.

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.

Carpathian Mathematical Publications

In the present paper, we study a new class of submanifolds of a generalized Quasi-Sasakian manifold, called skew semi-invariant submanifold. We obtain integrability conditions of the distributions on a skew semi-invariant submanifold and also find the condition for a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold to be mixed totally geodesic. Also it is shown that a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold will be anti-invariant if and only if $A_{\xi}=0$; and the submanifold will be skew semi-invariant submanifold if $\nabla w=0$. The equivalence relations for the skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold are given. Furthermore, we have proved that a skew semi-invariant $\xi^\perp$-submanifold of a normal almost contact metric manifold and a generalized Quasi-Sasakian manifold with non-trivial invariant distribution is $CR$-manifold. An example of dimension 5 is given to show that a skew s...

2019

We introduce the notion of trans-Sasakian Finsler manifold, then study semi-invariant submanifold F^m = (Y, Y\u27, F) of a trans-Sasakian Finsler manifold F^{2n+1} + (bar-Y, bar-Y\u27, bar-F) and we discuss the integrability conditions of the distrubitions of the semi-invariant submanifolds of the trans-Sasakian Finsler manifold

We define a seemi-symmetric metric connection in a nearly Sasakian manifold and we study semi-invariant sumanifolds of a nearly Sasakian manifold endowed with a semi-symmetric metric connection. Moreover, we discuss the integrability of adistribution on semi-invariant submanifolds.