Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


The rank in homogeneous spaces of nonpositive curvature

Author: María J. Druetta
Journal: Proc. Amer. Math. Soc. 105 (1989), 972-978
MSC: Primary 53C30
MathSciNet review: 946634
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a solvable and simply connected Lie group $ G$ with Lie algebra $ g$ and a left invariant metric of nonpositive curvature without flat factor, we prove that $ \operatorname{rank}(G) \leq \dim a$, where $ a$ is the orthogonal complement of $ [g,g]$ in $ g$. In particular, if $ H$ is a simply connected homogeneous space of nonpositive curvature satisfying the visibility axiom then $ H$ has rank one.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C30

Retrieve articles in all journals with MSC: 53C30

Additional Information

PII: S 0002-9939(1989)0946634-2
Keywords: Homogeneous spaces, nonpositive curvature, rank, visibility axiom
Article copyright: © Copyright 1989 American Mathematical Society