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The rank in homogeneous spaces of nonpositive curvature


Author: María J. Druetta
Journal: Proc. Amer. Math. Soc. 105 (1989), 972-978
MSC: Primary 53C30
DOI: https://doi.org/10.1090/S0002-9939-1989-0946634-2
MathSciNet review: 946634
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0946634-2
Keywords: Homogeneous spaces, nonpositive curvature, rank, visibility axiom
Article copyright: © Copyright 1989 American Mathematical Society

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