Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
ON THE GENERALIZED WINTGEN INEQUALITY FOR LEGENDRIAN SUBMANIFOLDS IN SASAKIAN SPACE FORMS
Ion Mihai
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2017 Volume 69 Issue 1 Pages 43-53

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Abstract

The generalized Wintgen inequality was conjectured by De Smet, Dillen, Verstraelen and Vrancken in 1999 for submanifolds in real space forms. It is also known as the DDVV conjecture. It was proven recently by Lu (2011) and by Ge and Tang (2008), independently. The present author established a generalized Wintgen inequality for Lagrangian submanifolds in complex space forms in 2014. In the present paper we obtain the DDVV inequality, also known as generalized Wintgen inequality, for Legendrian submanifolds in Sasakian space forms. Some geometric applications are derived. Also we state such an inequality for contact slant submanifolds in Sasakian space forms.

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© 2017 THE TOHOKU UNIVERSITY
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