Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms

Abstract

In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms.

Keywords

• Chen inequalities
• quarter-symmetric connection
• generalized Sasakian-space-form
• bi-slant
• Riemannian invariants