On the generalized Wintgen inequality for submanifolds in complex and Sasakian space forms

摘要

The normal scalar curvature conjecture, also known as the DDVV conjecture, was formulated by De Smet, Dillen, Verstraelen and Vrancken in 1999. It was proven recently by Lu [19] and by Ge and Tang [15] independently. Recently we obtained DDVV inequalities, also known as generalized Wintgen inequalities, for Lagrangian submanifolds in complex space forms and Legendrian submanifolds in Sasakian space forms, respectively. Some applications are given. Also we stated such inequalities for slant submanifolds in complex space forms and Sasakian space forms, respectively. Further developments are mentioned.