Chen-Type Inequality for Generic Submanifolds of Quaternionic Space Form and Its Application

Abstract

In 1993, the theory of Chen invariants started when Chen wrote basic inequalities for submanifolds in space forms. This inequality is called Chen’s first inequality. Afterward, many geometers studied many papers dealing with this new inequality. The present paper aims to establish a Chen inequality for quaternionic generic submanifolds in a quaternionic space form and obtain this inequality for real hypersurfaces.

Keywords

• chen-type inequality
• generic submanifold
• quaternionic space form
• real hypersurfaces