## Shyamal K. Hui, Richard S. Lemence, Pradip MandalWintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms

Comment.Math.Univ.Carolin. 61,1 (2020) 105-117.

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.

Keywords: generalized Sasakian-space-form; Legendrian submanifold

DOI: DOI 10.14712/1213-7243.2020.006
AMS Subject Classification: 53C25 53C15

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