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

Shyamal K. Hui; Richard S. Lemence; Pradip Mandal

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 1, page 105-117
  • ISSN: 0010-2628

Abstract

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A submanifold M m of a generalized Sasakian-space-form M ¯ 2 n + 1 ( f 1 , f 2 , f 3 ) is said to be C -totally real submanifold if ξ ∈ Γ ( T ⊥ M ) and φ X ∈ Γ ( T ⊥ M ) for all X ∈ Γ ( T M ) . 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.

How to cite

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Hui, Shyamal K., Lemence, Richard S., and Mandal, Pradip. "Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms." Commentationes Mathematicae Universitatis Carolinae 61.1 (2020): 105-117. <http://eudml.org/doc/297145>.

@article{Hui2020,
abstract = {A submanifold $M^m$ of a generalized Sasakian-space-form $\overline\{M\}^\{2n+1\}(f_1,f_2,f_3)$ 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.},
author = {Hui, Shyamal K., Lemence, Richard S., Mandal, Pradip},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {generalized Sasakian-space-form; Legendrian submanifold},
language = {eng},
number = {1},
pages = {105-117},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms},
url = {http://eudml.org/doc/297145},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Hui, Shyamal K.
AU - Lemence, Richard S.
AU - Mandal, Pradip
TI - Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 1
SP - 105
EP - 117
AB - A submanifold $M^m$ of a generalized Sasakian-space-form $\overline{M}^{2n+1}(f_1,f_2,f_3)$ 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.
LA - eng
KW - generalized Sasakian-space-form; Legendrian submanifold
UR - http://eudml.org/doc/297145
ER -

References

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