On the generalized Wintgen inequality for Legendrian submanifolds in Sasakian space forms
2017
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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