Chen’s Inequalities for Submanifolds in (<i>ĸ, &#181</i>)-Contact Space Form with a Semi-Symmetric Non-Metric Connection

Abstract

In this paper, we obtain Chen's inequalities in ( ) , κ µ -contact space form with a semi-symmetric non-metric connection. Also we obtain the inequalites for Ricci and K-Ricci curvatures.

Recent Developments on the First Chen Inequality in Differential Geometry

“…Remark 41. The corresponding first Chen inequalities for submanifolds in a (κ, µ)-contact space form endowed with a semisymmetric metric or nonmetric connection were derived in [168] and [169], respectively. Further, the inequality for submanifolds in (κ, µ)-contact space forms endowed with a generalized semisymmetric, nonmetric connection was obtained by Y. Wang in [170].…”