The rank in homogeneous spaces of nonpositive curvature

Druetta, María J.

doi:10.1090/S0002-9939-1989-0946634-2

The rank in homogeneous spaces of nonpositive curvature
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by María J. Druetta PDF

Proc. Amer. Math. Soc. 105 (1989), 972-978 Request permission

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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