Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms

Abstract

A submanifold $M^m$ of a generalized Sasakian-space-form $\overline{M}^{2n+1}(f_1,\allowbreak f_2,f_3)$ is said to be $C$-totally real submanifold if $\xi\in \Gamma(T^\bot M)$ and $\phi X\in \Gamma(T^\bot M)$ for all $X\in \Gamma(TM)$. In particular, if $m=n$, then $M^n$ is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.