A class of totally umbilical slant submanifolds of Lorentzian para-Sasakian manifolds (original) (raw)
On Pseudo-Slant Submanifolds of Nearly Quasi-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.
Submanifolds of a Lorentzian Para-Sasakian Manifold
2005
Recently, Matsumoto [1] introduced the notion of Lorentzian paracontact structure and studied its several properties. The object of the present paper is to study the submanifolds of Lorentzian para-Sasakian manifolds.
Warped Product Pointwise Semi-slant Submanifolds of Sasakian Manifolds
arXiv: Differential Geometry, 2017
Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using this notion, we investigate pointwise semi-slant submanifolds and their warped products in Sasakian manifolds. We give non-trivial examples of such submanifolds and obtain several fundamental results, including a characterization for warped product pointwise semi-slant submanifolds of Sasakian manifolds.
On pseudo-slant submanifolds of trans-Sasakian manifolds
Proceedings of the Estonian Academy of Sciences, 2011
The object of the present paper is to study pseudo-slant submanifolds of trans-Sasakian manifolds. Integrability conditions of the distributions on these submanifolds are worked out. Some interesting results regarding such manifolds have also been deduced. An example of a pseudo-slant submanifold of a trans-Sasakian manifold is given.
A note on totally umbilical proper slant submanifold of a Lorentzian beta-Kenmotsu manifold
Annals of the University of Craiova Mathematics and Computer Science Series, 2011
In the present note, we study a slant submanifold of a Lorentzian β-Kenmotsu manifold which is totally umbilical. We prove that every totally umbilical proper slant submanifold M of a Lorentzian β-Kenmotsu manifoldM is either minimal or if M is not minimal then we derive a formula for slant angle of M .
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.
Semi-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.
Warped Product Semi-Slant Submanifolds of a Sasakian Manifold
Serdica. Mathematical Journal, 2008
In the present note, it is proved that there donot exist warped product semi-slant submanifolds in a Sasakian manifold other than contact CR-warped product submanifolds and thus the results obtained in [8] are generalized.