On the surfaces of revolution with constant mean curvature in the hyperbolic space

DOI10.5802/AFST.903zbMath0921.53029OpenAlexW4311918545MaRDI QIDQ1284675

Philippe Castillon

Publication date: 25 May 1999

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_1998_6_7_3_379_0

zbMATH Keywords

constant mean curvature surfaceshyperbolic rotational surfacessurfaces in hyperbolic 3-space

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Non-Euclidean differential geometry (53A35)

Cites Work

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• A generalization of a theorem of Delaunay to rotational W-hypersurfaces of \(\sigma _{\ell}\)-type in \(H^{n+1}\) and \(S^{n+1}\)
• On generalization of theorems of A. D. Alexandrov and C. Delaunay on hypersurfaces of constant mean curvature
• The geometry of properly embedded special surfaces in \(\mathbb{R}^ 3\); e.g., surfaces satisfying \(aH+bK=1\), where \(a\) and \(b\) are positive
• A generalization of a theorem of Delaunay
• Spherical surfaces with constant mean curvature in hyperbolic space
• Geometry and spectra of compact Riemann surfaces

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