Minimal orbits at infinity in homogeneous spaces of nonpositive curvature

María J. Druetta

Vol. 156 (1992), No. 2, 287–296

DOI: 10.2140/pjm.1992.156.287

Abstract

Let M denote a simply connected, homogeneous space of nonpositive curvature and let G be the connected component of the identity of the isometry group of M.

In this paper we study the geometric consequences on M if M(∞), the boundary sphere of M, admits a G-orbit whose closure is a minimal set for G. A characterization of symmetric spaces of noncompact type in terms of the action of G in M(∞), is obtained. As an application we give some conditions, in terms of the Lie algebra of a simply transitive and solvable subgroup of G that is in standard position, which are equivalent to the fact that M is a symmetric space.

Mathematical Subject Classification 2000

Primary: 53C30

Secondary: 53C35

Milestones

Received: 1 January 1991

Revised: 14 August 1991

Published: 1 December 1992