Contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold

Abstract

In this paper we prove some properties of the indefinite Lorentzian para-Sasakian manifolds. Section 1 is introductory. In Section 2 we define D-totally geodesic and D⊥-totally geodesic contact CRsubmanifolds of an indefinite Lorentzian para-Sasakian manifold and deduce some results concerning such a manifold. In Section 3 we state and prove some results on mixed totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. Finally, in Section 4 we obtain a result on the anti-invariant distribution of totally umbilic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold.

Keywords

• and phrases contact cr-submanifold
• totally umbilic submanifold
• indefinite lorentzian para-sasakian manifold
• d-totally geodesic
• d⊥-totally geodesic
• mixed totally geodesic
• anti invariant distribution d⊥