Contact CR-Warped Product Submanifolds of Nearly Lorentzian Para-Sasakian Manifolds

Abstract

In the present paper we have investigated CR-submanifold of a nearly Lorentzian para-Sasakian manifolds, generalizing sharp inequality namely $||h||^{2}\geq \frac{2}{9} s +2s ||\nabla \ln f||^{2}$, for contact CR-warped products of nearly Lorentzian para-Sasakian manifolds. It is also proved that the derive inequalities for contact CR-warped products either in any contact metric manifold. The equality case is also handled.

Keywords

• CR-submanifold,nearly Lorentzian para-Sasakian manifold,$\xi$-vertical CR-submanifold.

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