Real and complex k-planes in convex hypersurfaces

[摘要] It is shown that if the rank of the second fundamental form (resp. the Levi form) of a C-2-smooth convex hypersurface M in Rn+1 (resp. Cn+1) does not exceed an integer constant k < n near a point p is an element of M, then through any point q is an element of M near p there exists a real (resp. complex) (n - k)-dimensional plane that locally lies on M. (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] Convex hypersurface;Levi form