Hypersurfaces with constant mean curvature in the complex hyperbolic space
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- by Susana Fornari, Katia Frensel and Jaime Ripoll PDF
- Trans. Amer. Math. Soc. 339 (1993), 685-702 Request permission
Erratum: Trans. Amer. Math. Soc. 347 (1995), 3177.
Abstract:
A classical theorem of A. D. Alexandrov characterized round spheres is extended to the complex hyperbolic space ${\mathbf {C}}{{\mathbf {H}}^2}$ of constant holomorphic sectional curvature. A detailed description of the horospheres and equidistant hypersurfaces in ${\mathbf {C}}{{\mathbf {H}}^2}$ determining in particular their stability, is also given.References
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- Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR 0238225 B. O’Neill, The fundamental equations of a Riemannian submersion, Michigan Math. J. 23 (1966), 459-469.
- Barrett O’Neill, Semi-Riemannian geometry, Pure and Applied Mathematics, vol. 103, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. With applications to relativity. MR 719023
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 339 (1993), 685-702
- MSC: Primary 53C42; Secondary 53C40
- DOI: https://doi.org/10.1090/S0002-9947-1993-1123452-1
- MathSciNet review: 1123452