Groups, Geometry, and Dynamics


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Volume 11, Issue 1, 2017, pp. 1–27
DOI: 10.4171/GGD/385

Published online: 2017-04-20

A splitting theorem for spaces of Busemann non-positive curvature

Alon Pinto[1]

(1) The Weizmann Institute of Science, Rehovot, Israel

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.

Keywords: Busemann spaces, Finsler manifolds, Clifford isometries, product decompositions, uniform convexity, splitting theorem

Pinto Alon: A splitting theorem for spaces of Busemann non-positive curvature. Groups Geom. Dyn. 11 (2017), 1-27. doi: 10.4171/GGD/385