Certain basic inequalities for submanifolds of locally conformal Kaehler space forms

Abstract

Certain basic inequalities, involving the squared mean curvature and one of the scalar curvature, the sectional curvature and the Ricci curvature for a submanifold of any Riemannian manifold, are obtained. Applying these results we obtain the corresponding inequalities for different kinds of submanifolds of a locally conformal Kaehler space form. Equality cases are also discussed. Finally, we also find a sufficient condition for a Lagrangian submanifold of a locally conformal Kaehler space form to be minimal.