Visibility and rank one in homogeneous spaces of 𝐾≤0

Druetta, María J.

doi:10.1090/S0002-9947-1987-0906817-7

Visibility and rank one in homogeneous spaces of $K\leq 0$
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by María J. Druetta PDF

Trans. Amer. Math. Soc. 304 (1987), 307-321 Request permission

Abstract:

In this paper we study relationships between the visibility axiom and rank one in homogeneous spaces of nonpositive curvature. We obtain a complete classification (in terms of rank) of simply connected homogeneous spaces of nonpositive curvature and dimension $\leqslant 4$. We provide examples, in every $\dim \geqslant 4$, of simply connected, irreducible homogeneous spaces $(K \leqslant 0)$ which are neither visibility manifolds nor symmetric spaces.

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