Hypersurfaces with constant mean curvature in hyperbolic space form

Jean-Marie Morvan*, Bao Qiang Wo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this article, we prove the following theorem: A complete hypersurface of the hyperbolic space form, which has constant mean curvature and non-negative Ricci curvature Q, has non-negative sectional curvature. Moreover, if it is compact, it is a geodesic distance sphere; if its soul is not reduced to a point, it is a geodesic hypercylinder; if its soul is reduced to a point p, its curvature satisfies ∥∇Q∥ < ∞, and the geodesic spheres centered at p are convex, then it is a horosphere.

Original languageEnglish (US)
Pages (from-to)197-222
Number of pages26
JournalGeometriae Dedicata
Volume59
Issue number2
DOIs
StatePublished - Jan 1 1996

Keywords

  • Hyperbolic space
  • Hypersurfaces
  • Ricci curvature

ASJC Scopus subject areas

  • Geometry and Topology

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