On the $Hp$-theorem for hypersurfaces

Giovanni Rotondaro

Displaying similar documents to “On the $H p$ -theorem for hypersurfaces”

Compact hypersurfaces with constant higher order mean curvatures.

Antonio Ros Mulero (1987)

Revista Matemática Iberoamericana

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A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature H, for some r = 1, ..., n.

Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space

Qiaoling Wang, Chang Yu Xia (2007)

Czechoslovak Mathematical Journal

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In this paper we study the topological and metric rigidity of hypersurfaces in $ℍ^{n + 1}$ , the $(n + 1)$ -dimensional hyperbolic space of sectional curvature $- 1$ . We find conditions to ensure a complete connected oriented hypersurface in $ℍ^{n + 1}$ to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface with constant norm of the second fundamental form to be totally umbilic.