Remarks on an Inequality involving the Normal Scalar Curvature

Abstract

Abstract. We study a pointwise inequality for submanifolds in real space forms involving the scalar curvature, the normal scalar curvature and the mean curvature, which is up to now only proven in some special cases. We translate it to an algebraic problem, allowing us to prove a slightly weaker version of it. Further we improve the classification of codimension 2-immersions realizing the equality at every point, and we prove the inequality for some classes of Lagrangian submanifolds of C n. 1.