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2 results

  • geometrical versus topological properties of manifolds

  • carlos matheus, krerley oliveira
  • Journal:
    Journal of the Institute of Mathematics of Jussieu / Volume 4 / Issue 4 / October 2005
    Published online by Cambridge University Press:
    09 May 2005, pp. 639-651
    Print publication:
    October 2005

  • given a compact $n$-dimensional immersed riemannian manifold $m^n$ in some euclidean space we prove that if the hausdorff dimension of the singular set of the gauss map is small, then $m^n$ is homeomorphic to the sphere $s^n$.

    also, we define a concept of finite geometrical type and prove that finite geometrical type hypersurfaces with a small set of points of zero gauss–kronecker curvature are topologically the sphere minus a finite number of points. a characterization of the $2n$-catenoid is obtained.