Characterizing horospheres of the hyperbolic space via higher order mean curvatures

DOI10.1016/j.difgeo.2018.10.004zbMath1410.53056OpenAlexW2899990567WikidataQ115355038 ScholiaQ115355038MaRDI QIDQ1733249

Halyson I. Baltazar, Henrique Fernandes de Lima, Cicero Pedro Aquino

Publication date: 21 March 2019

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2018.10.004

zbMATH Keywords

hyperbolic spacehorospherescomplete two-sided hypersurfaceshigher-order mean curvatureshyperbolic cylinders

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global Riemannian geometry, including pinching (53C20)

Related Items

Uniqueness and nullity of complete spacelike hypersurfaces immersed in the anti-de Sitter space ⋮ Nomizu-Smyth type results in the hyperbolic and De Sitter spaces via Gauss-Kronecker curvature ⋮ Revisiting the geometry of horospheres of the hyperbolic space ⋮ Horosphere slab separation theorems in manifolds without conjugate points

Cites Work

• Unnamed Item
• Unnamed Item
• The geometry of closed conformal vector fields on Riemannian spaces
• On the geometry of horospheres
• On the Gauss map of complete CMC hypersurfaces in the hyperbolic space
• On Alexandrov-Bernstein theorems in hyperbolic space
• Complete vertical graphs with constant mean curvature in semi-Riemannian warped products
• Existence of constant mean curvature graphs in hyperbolic space
• Constant positive 2-mean curvature hypersurfaces
• On the Gauss mapping of hypersurfaces with constant scalar curvature in \(\mathbb H^{n+1}\)
• Hadamard-type theorems for hypersurfaces in hyperbolic spaces
• Uniqueness of constant mean curvature surfaces properly immersed in a slab
• A special Stoke's theorem for complete Riemannian manifolds
• Bernstein-type theorems in semi-Riemannian warped products
• Embedded positive constant r-mean curvature hypersurfaces in Mm × R
• Complete CMC hypersurfaces in the hyperbolic space with prescribed Gauss mapping
• CONSTANT HIGHER-ORDER MEAN CURVATURE HYPERSURFACES IN RIEMANNIAN SPACES
• On Stokes' Theorem for Noncompact Manifolds
• Unicity of constant mean curvature hypersurfaces in some riemannian manifolds
• INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONS