On the generalized Wintgen inequality for Lagrangian submanifolds in complex space forms

The normal scalar curvature conjecture, also known as the DDVV conjecture, was formulated by De Smet et al. (1999). It was proven recently by Lu (2011) and by Ge and Tang (2008) independently.We obtain the DDVV inequality, also known as the generalized Wintgen inequality, for Lagrangian submanifolds in complex space forms. Some applications are given. Also we state such an inequality for slant submanifolds in complex space forms.