Geodesic
Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 105-117.

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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.
DOI : 10.14712/1213-7243.2020.006
Classification : 53C15, 53C25
Keywords: generalized Sasakian-space-form; Legendrian submanifold 
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Hui, Shyamal K.; Lemence, Richard S.; Mandal, Pradip. Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 105-117. doi : 10.14712/1213-7243.2020.006. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.006/

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