Some Basic Inequalities on (<em>ϵ</em>)-Para Sasakian Manifold

Abstract

We propose fundamental inequalities for contact pseudo-slant submanifolds of (ϵ)-para Sasakian space form employing generalized normalized δ-Casorati curvature. We characterize submanifolds for which equality cases hold and illustrate the main result with some applications. Further, we have considered a certain type of submanifold for a Ricci soliton and after computing its scalar curvature, developed an inequality to find correlations between intrinsic or extrinsic invariants.

Keywords

• para-Sasakian manifold
• (ϵ)-para Sasakian space form
• δ-Casorati curvature
• scalar curvature
• Ricci soliton
• contact pseudo-slant submanifold