Nonpositively curved homogeneous spaces of dimension five

María J. Druetta

Vol. 148 (1991), No. 1, 17–37

DOI: 10.2140/pjm.1991.148.17

Abstract

In this paper we classify, in terms of the rank, the simply connected homogeneous spaces of nonpositive curvature and dimension five. In particular, an affirmative answer is given to the conjecture “An irreducible homogeneous space of nonpositive curvature and rank k ≥ 2 is a symmetric space of rank k”.

We exhibit examples in dimension five of rank one homogeneous spaces of nonpositive curvature having totally geodesic two-flats isometrically imbedded. Moreover, these examples show that the rank in a Lie group is not invariant under the change of left invariant metrics of nonpositive curvature

Mathematical Subject Classification 2000

Primary: 53C30

Secondary: 53C21

Milestones

Received: 11 April 1989

Revised: 31 January 1990

Published: 1 March 1991