Isometric immersions in the hyperbolic space with their image contained in a horoball
type: Item
instance of: scholarly article
zbMATH Open document ID: 0979.53066
DOI: 10.1017/S0017089501000015
author: Ana Lluch
published in: Glasgow Mathematical Journal
publication date: 2001-08-19T00:00:00Z
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1615389
zbMATH Keywords: codimension-1 immersion
zbMATH Keywords: real and complex hyperbolic space
zbMATH Keywords: horoball
zbMATH Keywords: mean curvature
MaRDI profile type: Publication
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title: Isometric immersions in the hyperbolic space with their image contained in a horoball
review text: Suppose that \(M\) is a complete Riemannian manifold with scalar curvature bounded from below. If \(M\) has an isometric, codimension-1 immersion into a horoball of a real or complex hyperbolic space, then the author proves a sharp lower bound for the supremum of the norm of the mean curvature. The author next characterizes horospheres in real or complex hyperbolic space as those proper isometric, codimension-1 immersions of a complete Riemannian manifold whose image is contained between two parallel horospheres, whose mean curvature is bounded from above by the sharp lower bound already discussed, and whose group of symmetries is sufficiently large.
reviewed by: James Hebda
description: scientific article; zbMATH DE number 1615389