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On slant submanifolds of neutral Kähler manifolds. (English) Zbl 1202.53022
Summary: An indefinite Riemannian manifold is called neutral it its index is equal to one half of its dimension and an indefinite Kähler manifold is called neutral Kähler 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 Kähler surfaces to slant submanifolds in neutral Kähler 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.
MSC:
53B25Local submanifolds
53C40Global submanifolds (differential geometry)
53C42Immersions (differential geometry)