A splitting theorem for spaces of Busemann non-positive curvature
Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 1-27
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In this paper we introduce a new tool for decomposing Busemann non-positively curved (BNPC) spaces as products, and use it to extend several important results previously known to hold in specific cases like CAT(0) spaces. These results include a product decomposition theorem, a de Rham decomposition theorem, and a splitting theorem for actions of product groups on certain BNPC spaces. We study the Clifford isometries of BNPC spaces and show that they always form Abelian groups, answering a question raised by Gelander, Karlsson, and Margulis. In the smooth case of BNPC Finsler manifolds, we show that the fundamental groups have the duality property and generalize a splitting theorem previously known in the Riemannian case.
Classification :
20-XX, 53-XX
Mots-clés : Busemann spaces, Finsler manifolds, Clifford isometries, product decompositions, uniform convexity, splitting theorem
Mots-clés : Busemann spaces, Finsler manifolds, Clifford isometries, product decompositions, uniform convexity, splitting theorem
Affiliations des auteurs :
Alon Pinto 1
Alon Pinto. A splitting theorem for spaces of Busemann non-positive curvature. Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 1-27. doi: 10.4171/ggd/385
@article{10_4171_ggd_385,
author = {Alon Pinto},
title = {A splitting theorem for spaces of {Busemann} non-positive curvature},
journal = {Groups, geometry, and dynamics},
pages = {1--27},
year = {2017},
volume = {11},
number = {1},
doi = {10.4171/ggd/385},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/385/}
}
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