Geometrical versus Topological Properties of Manifolds
نویسنده
چکیده
Given a compact n-dimensional immersed Riemannian manifold Mn in some Euclidean space we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, then Mn is homeomorphic to the sphere Sn. Also, we define a concept of finite geometrical type and prove that finite geometrical type hypersurfaces with small set of points of zero GaussKronecker curvature are topologically the sphere minus a finite number of points. A characterization of the 2n-catenoid is obtained.
منابع مشابه
Geometrical versus Topological Properties of Manifolds and a Remark on Poincaré Conjecture
Given a compact n-dimensional immersed Riemannian manifold Mn we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, then Mn is homeomorphic to the sphere Sn. A consequence of our main theorems is a conjecture which is equivalent to Poincaré Conjecture. Also, we define a concept of finite geometrical type and prove that finite geometrical type hypersurfaces are ...
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تاریخ انتشار 2003