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Tits geometry associated with 4-dimensional closed real-analytic manifolds of nonpositive curvature


Hummel, C; Schroeder, V (1998). Tits geometry associated with 4-dimensional closed real-analytic manifolds of nonpositive curvature. Journal of Differential Geometry, 48(3):531-555.

Abstract

We investigate the geometry and topology of the Tits boundary associated with 4-dimensional closed, real-analytic manifolds of nonpositive curvature. We show that each homotopically nontrivial component is a union of geometric boundaries of flats in the corresponding Hadamard manifold and this can be used to describe the structure of its maximal dimensional quasi-flats. The homotopically trivial components are intervals of length smaller than π and we give a necessary and sufficient criterion for the existence of such intervals of length grater than zero.

Abstract

We investigate the geometry and topology of the Tits boundary associated with 4-dimensional closed, real-analytic manifolds of nonpositive curvature. We show that each homotopically nontrivial component is a union of geometric boundaries of flats in the corresponding Hadamard manifold and this can be used to describe the structure of its maximal dimensional quasi-flats. The homotopically trivial components are intervals of length smaller than π and we give a necessary and sufficient criterion for the existence of such intervals of length grater than zero.

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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
Language:English
Date:1998
Deposited On:29 Nov 2010 16:28
Last Modified:06 Dec 2017 20:57
Publisher:Lehigh University
ISSN:0022-040X
Free access at:Official URL. An embargo period may apply.
Official URL:http://www.intlpress.com/journals/JDG/archive/vol.48/3_5.pdf
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0920.53021
http://www.ams.org/mathscinet-getitem?mr=1638057
http://projecteuclid.org/euclid.jdg/1214460862

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