On slant submanifolds of neutral Kaehler manifolds

Abstract

An indefinite Riemannian manifold is called neutral it its index is equal to one half of its dimension and an indefinite Kaehler manifold is called neutral Kaehler if its complex index is equal to the half of its complex dimension. In the first part of this article, we extend the notion of slant surfaces in Lorentzian Kaehler surfaces to slant submanifolds in neutral Kaehler manifolds; moreover, we characterize slant submanifolds with parallel canonical structures. By applying the results obtained in the first part we completely classify slant surfaces with parallel mean curvature vector and minimal slant surfaces in the Lorentzian complex plane in the second part of this article.