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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


The Euclidean factor of a Hadamard manifold

Authors: Toshiaki Adachi and Fumiko Ohtsuka
Journal: Proc. Amer. Math. Soc. 113 (1991), 209-212
MSC: Primary 53C20; Secondary 53C23
MathSciNet review: 1074746
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Abstract: The ideal boundary $ X(\infty )$ of a Hadamard manifold $ X$ is the set of asymptotic classes of rays on $ X$. We shall characterize the Euclidean factor of $ X$ by information on $ X(\infty )$. Under the assumption that the diameter of $ X(\infty )$ is $ \pi $, we call a boundary point that has a unique point of Tits distance $ \pi $ a polar point. We shall show that such points form a standard sphere and compose the boundary of the Euclidean factor of the given Hadamard manifold.

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PII: S 0002-9939(1991)1074746-3
Keywords: Euclidean factor, Tits metric, polar point, Hadamard manifold
Article copyright: © Copyright 1991 American Mathematical Society