On pseudo-slant submanifolds of trans-Sasakian manifolds

Mathematical Physics and Computer Simulation, 2019

The geometry of pseudo-slant submanifolds of nearly quasi Sasakian manifold is studied. It is proved that totally umbilical proper-slant submanifold of nearly quasi Sasakian manifold admits totally geodesic if the mean curvature vector ∈ µ. The integrability conditions of the distributions of pseudo-slant submanifolds of nearly quasi Sasakian manifold are also obtained.

The Bulletin of Society for Mathematical Services and Standards, 2015

In this paper we would like to establish some of the properties of slant and hemislant submanifolds of an indefinite trans-Sasakian manifold. We have four sections in this paper. Section (1) is introductory. In Section (2) we recall some necessary details of an indefinite trans-Sasakian manifold. In Section (3) we have obtained some interesting properties on a totally umbilical slant submanifolds of an indefinite trans-Sasakian manifold. Finally, in Section (4), some results on integrability conditions of the distributions of hemislant submanifolds of an indefinite trans-Sasakian manifold have been obtained.

JOURNAL OF ADVANCES IN MATHEMATICS

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a Sasakian manifold. We derive the integrability conditions of distributions in the definition of a contact pseudo-slant submanifold. The notions contact pseudo-slant product is defined, and the necessary and sufficient conditions for a submanifold to contact pseudo-slant product is given. Also, a non-trivial example is used to demonstrate that the method presented in this paper is effective.

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. ...

Differential Geometry-Dynamical …, 2011

In this paper, we study slant and hemi-slant submanifolds of nearly trans-Sasakian manifolds. We obtain the necessary and sufficient conditions on a totally umbilical proper slant submanifold and show that it is totally geodesic if the mean curvature vector H ∈ µ. As well, we obtain the integrability conditions of the distributions of hemi-slant submanifolds and prove some characterization theorems.

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2018

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a Sasakian manifold. We verify some properties of the components of the tensor field acting on that kind of submanifold and find out the necessary and sufficient conditions for them to be parallel. Also, necessary and sufficient conditions are given for a submanifold to be a pseudo-slant submanifold, contact pseudo-slant product, D θ , D ⊥ and mixed-geodesic in Sasakian manifold.

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.

Mediterranean Journal of Mathematics, 2015

In this paper, we introduce the notion of screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2 and RadT M on screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds have been obtained. Further, we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic. We also study mixed geodesic screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds.

Kyungpook mathematical journal, 2016

In this paper, we introduce the notion of semi-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2 and RadT M on semi-slant lightlike submanifolds of an indefinite Sasakian manifold have been obtained. We also obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.

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...