Showing papers by "David E. Blair published in 1996"

Hypersurfaces of restricted type in Minkowski space

Abstract: A submanifold Mnr of Minkowski space \(\mathbb{E}_1^m \) is said to be of restricted type if its shape operator with respect to the mean curvature vector is the restriction of a fixed linear transformation of \(\mathbb{E}_1^m \) to the tangent space of Mnr at every point of Mnr. In this paper we completely classify hypersurfaces of restricted type in \(\mathbb{E}_1^{n + 1} \). More precisely, we prove that a hypersurface of \(\mathbb{E}_1^m \) is of restricted type if and only if it is either a minimal hypersurface, or an open part of one of the following hypersurfaces: Sk × \(\mathbb{E}_1^{n - k} \), Sk1 × \(\mathbb{E}^{n - k} \), Hk × \(\mathbb{E}^{n - k} \), Sn1, Hn, with 1≤k≤n−1, or an open part of a cylinder on a plane curve of restricted type.

On a type of real hypersurfaces in complex projective space

Abstract: We give a classification of real hypersurfaces in complex proiective space under assumptions that the structure vector t is principal, the focal map has constant rank and that V f = o, where C is the Weyl conformal curvature tensor of the real hvoersurface.