A splitting theorem for spaces of Busemann non-positive curvature (Q2357399)

Summary: 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 \textit{T. Gelander} et al. [Geom. Funct. Anal. 17, No. 5, 1524--1550 (2008; Zbl 1156.22005)]. 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.