Geometrical versus Topological Properties of Manifolds and a Remark on Poincaré Conjecture
نویسنده
چکیده
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 topologically the sphere minus a finite number of points. A characterization of the 2n-catenoid is obtained.
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