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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Visibility and rank one in homogeneous spaces of $ K\leq 0$


Author: María J. Druetta
Journal: Trans. Amer. Math. Soc. 304 (1987), 307-321
MSC: Primary 53C30
DOI: https://doi.org/10.1090/S0002-9947-1987-0906817-7
MathSciNet review: 906817
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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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DOI: https://doi.org/10.1090/S0002-9947-1987-0906817-7
Keywords: Homogeneous spaces, visibility manifolds, rank
Article copyright: © Copyright 1987 American Mathematical Society