Optimal Inequalities for Submanifolds in Trans-Sasakian Manifolds Endowed with a Semi-Symmetric Metric Connection

Abstract

In this paper, we improve the Chen first inequality for special contact slant submanifolds and Legendrian submanifolds, respectively, in (α,β) trans-Sasakian generalized Sasakian space forms endowed with a semi-symmetric metric connection.

Keywords

• Chen inequality
• Sasakian space form
• special contact slant submanifold
• Legendrian submanifold
• semi-symmetric metric connection