Tohoku Mathematical Journal
2017
March
SECOND SERIES VOL. 69, NO. 1

Tohoku Math. J.
69 (2017), 43-53

Title ON THE GENERALIZED WINTGEN INEQUALITY FOR LEGENDRIAN SUBMANIFOLDS IN SASAKIAN SPACE FORMS

Author Ion Mihai

(Received November 12, 2014, revised May 15, 2015)
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.

Mathematics Subject Classification. Primary 53C40; Secondary 53C25, 53D10.
Key words and phrases. Wintgen inequality, DDVV conjecture, Sasakian space form, invariant submanifold, Legendrian submanifold, contact slant submanifold.

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