On Hypersurfaces of Hyperbolic Space Infinitesimally Supported by Horospheres

DOI10.2307/2001083zbMath0679.53045OpenAlexW4248073309MaRDI QIDQ4728956

Robert J. Currier

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001083

zbMATH Keywords

second fundamental formhypersurfaceconvex bodyhorospherehyperbolic space form

Mathematics Subject Classification ID

Global submanifolds (53C40) Spherical and hyperbolic convexity (52A55)

Related Items (17)

On nonnegatively curved hypersurfaces in \(\mathbb{H}^{n+1}\) ⋮ Locally convex surfaces immersed in a Killing submersion ⋮ Embeddedness, convexity, and rigidity of hypersurfaces in product spaces ⋮ Nonnegatively curved hypersurfaces with free boundary on a sphere ⋮ On the Gauss map of equivariant immersions in hyperbolic space ⋮ Convexity, rigidity, and reduction of codimension of isometric immersions into space forms ⋮ Some remarks on convex surfaces in simply connected homogeneous three manifolds ⋮ Evolution of graphs in hyperbolic space by their Gauss curvature ⋮ When strictly locally convex hypersurfaces are embedded ⋮ Constant mean curvature graphs on exterior domains of the hyperbolic plane ⋮ Hypersurfaces with nonegative Ricci curvature in \(\mathbb {H}^{n+1}\) ⋮ Locally convex hypersurfaces immersed in \(\mathbb {H}^n\times \mathbb {R}\) ⋮ On a class of immersions of spheres into space forms of nonpositive curvature ⋮ Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds ⋮ On locally convex hypersurfaces in Hadamard manifolds ⋮ Mixed volume preserving flow by powers of homogeneous curvature functions of degree one ⋮ Hypersurfaces in hyperbolic space with support function

Cites Work

• Unnamed Item
• Completeness of curvature surfaces of an isometric immersion
• Rigidity and convexity of hypersurfaces in spheres
• The behavior of a function on its critical set
• Isometric immersions into manifolds without conjugate points
• Immersions with Semi-Definite Second Fundamental Forms
• Immersions of manifolds with non-negative sectional curvatures
• Locally Convex Hypersurfaces of Negatively Curved Spaces
• On Hypersurfaces with no Negative Sectional Curvatures
• On locally convex manifolds

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