ON SLANT SURFACES

Abstract

A slant immersion was introduced in [1] as an isometric immersion of a Riemannian manifold into an almost Hermitian manifold with constant Wirtinger angle. It is known that there exist ample examples of slant submanifolds; in particular, slant surfaces in complex-spaceforms. In this paper, we establish a sharp inequality for slant surfaces and determine the Riemannian structures of special slant surfaces in complexspace- forms. By applying the special forms of the Riemannian structures on special slant surfaces we prove that proper slant surfaces in C2 are minimal if and only if they are special slant. We also determine proper slant surfaces in complex-space-forms which satisfy the equality case of the inequality identically.