ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE
DOI10.1017/S1446788716000549zbMath1379.53079MaRDI QIDQ4591202
Márcio Batista, Cicero Pedro Aquino, Henrique Fernandes de Lima
Publication date: 13 November 2017
Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)
hyperbolic spacecomplete hypersurfaceshigher-order mean curvaturestotally umbilical hypersurfacesLorentzian Gauss map
Applications of differential geometry to physics (53Z05) General relativity (83C99) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)
Cites Work
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- 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
- Stability of hypersurfaces with constant \(r\)-mean curvature
- Variational properties of functions of the mean curvatures for hypersurfaces in space forms
- Integral formulas for compact space-like hypersurfaces in de Sitter space: Applications to the case of constant higher order mean curvature
- 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
- Bernstein-type theorems in semi-Riemannian warped products
- Complete CMC hypersurfaces in the hyperbolic space with prescribed Gauss mapping
- Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space
- On Stokes' Theorem for Noncompact Manifolds
- Unicity of constant mean curvature hypersurfaces in some riemannian manifolds
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