A General Inequality for Kählerian Slant Submanifolds and Related Results

Abstract

An isometric immersion of a Riemannian manifold into a Kahlerian manifold is called slant if it has a constant Wirtinger angle. A slant submanifold is called Kahlerian slant if its canonical structure is parallel. In this article, we prove a general inequality relating the mean and scalar curvatures of Kahlerian slant submanifolds in a complex space form. We also classify Kahlerian slant submanifolds which satisfy the equality case of the inequality. Several related results on slant submanifolds are also proved.