An Inequality for Warped Product Semi-Invariant Submanifolds of a Normal Paracontact Metric Manifold

Abstract

The aim of this paper is to study the warped product semi-invariant submanifolds in a normal
paracontact metric space form. We obtain some characterization and new geometric obstructions for
the warped product type M? f MT. We establish a general inequality among the trace of the induced
tensor, laplace operator, the squared norms of the second fundamental form and warping function . These
inequalities are discussed and we obtain some new results.