Hyperbolic characteristics on star-shaped hypersurfaces
نویسندگان
چکیده
منابع مشابه
Star points on smooth hypersurfaces
— A point P on a smooth hypersurface X of degree d in PN is called a star point if and only if the intersection of X with the embedded tangent space TP (X) is a cone with vertex P . This notion is a generalization of total inflection points on plane curves and Eckardt points on smooth cubic surfaces in P3. We generalize results on the configuration space of total inflection points on plane curv...
متن کاملNote on Star-shaped Sets
1. The aim of this note is to prove that if 717" is a compact subset of En and for some m every w-dimensional hyperplane through a fixed point pQEn intersects M along a nonempty acyclic set, lúm^n — 1, then M is star-shaped with respect to p, i.e., if aQM then the segment pa is contained in M. This theorem is a generalization of a theorem of Aumann [l]. We gave recently a proof of Aumann's theo...
متن کاملSingularity analysis of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces
This paper introduces the notions of pseudo null curves in Minkowski 4-space. Meanwhile, some geometrical characterizations and the singularities of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces, which are generated by pseudo null curves, are considered in this paper. c ©2016 All rights reserved.
متن کاملHomogeneous Hypersurfaces in Complex Hyperbolic Spaces
We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.
متن کاملOn Convexity of Hypersurfaces in the Hyperbolic Space
In the Hyperbolic space Hn (n ≥ 3) there are uncountably many topological types of convex hypersurfaces. When is a locally convex hypersurface in Hn globally convex, that is, when does it bound a convex set? We prove that any locally convex proper embedding of an (n− 1)-dimensional connected manifold is the boundary of a convex set whenever the complement of (n−1)-flats of the resulting hypersu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 1999
ISSN: 0294-1449
DOI: 10.1016/s0294-1449(00)88185-8