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The hyperbolic rank of homogeneous Hadamard manifolds


Foertsch, T (2002). The hyperbolic rank of homogeneous Hadamard manifolds. Manuscripta Mathematica, 109(1):109-120.

Abstract

 From results in [BrFa] it follows that for Riemannian products of real hyperbolic spaces the sum of the Euclidean rank and the hyperbolic rank is at least the product's dimension. In [Leu] the author proved that, more generally, the same holds for symmetric spaces of non-compact type. In this paper we prove the analogue statement for arbitrary homogeneous Hadamard manifolds.

Abstract

 From results in [BrFa] it follows that for Riemannian products of real hyperbolic spaces the sum of the Euclidean rank and the hyperbolic rank is at least the product's dimension. In [Leu] the author proved that, more generally, the same holds for symmetric spaces of non-compact type. In this paper we prove the analogue statement for arbitrary homogeneous Hadamard manifolds.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Hadamard manifold; homogeneous spaces; rank; geodesic hyperbolic spaces
Language:English
Date:2002
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Springer
ISSN:0025-2611
Publisher DOI:https://doi.org/10.1007/s00229-002-0294-8
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1020.53017
http://www.ams.org/mathscinet-getitem?mr=1931212

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