Generalized Wintgen inequalities for submanifolds of conformally flat manifolds

Abstract

We obtain generalized Wintgen inequalities for submanifolds of conformally flat manifolds. As applications, we derive corresponding inequalities for submanifolds of Riemannian manifolds of quasi-constant curvature, generalized Robertson--Walker type warped products, conformally changed real space forms, and products of real space forms with opposite curvatures. Equality cases are also discussed. Moreover, several obstructions to the existence of minimal submanifolds are obtained from these inequalities.