On Curvatures of Semi-invariant Submanifolds of Lorentzian Para-Sasakian Manifolds

Abstract

A Lorentzian para-Sasakian (LP-Sasakian) space form is a kind of para-Sasakian manifold with constant $ \varphi- $ holomorphic sectional curvature. The presented paper is on the curvatures of semi-invariant submanifolds of a LP-Sasakian space form. Firstly, the definition of a semi-invariant submanifold of LP-Sasakian space form is given and an example is presented. Then, using Gauss equation related to curvatures used for obtaining some important results on Ricci and scalar curvatures. Moreover, by suffering from these results conditions of distributions being Einstein have been examined. Finally, semi-invariant products of Lorentzian para-Sasakian manifolds have been considered and an important inequality for second fundamental form is proved.