Neeb KH (2002)
Publication Type: Journal article, Original article
Publication year: 2002
Publisher: Springer Verlag (Germany)
Book Volume: 95
Pages Range: 115-156
Journal Issue: 1
In this paper we study Banach–Finsler manifolds endowed with a spray which have seminegative curvature in the sense that the corresponding exponential function has a surjective expansive differential in every point. In this context we generalize the classical theorem of Cartan–Hadamard, saying that the exponential function is a covering map. We apply this to symmetric spaces and thus obtain criteria for Banach–Lie groups with an involution to have a polar decomposition. Typical examples of symmetric Finsler manifolds with seminegative curvature are bounded symmetric domains and symmetric cones endowed with their natural Finsler structure which in general is not Riemannian.
APA:
Neeb, K.H. (2002). A Cartan–Hadamard Theorem for Banach–Finsler Manifolds. Geometriae Dedicata, 95(1), 115-156. https://dx.doi.org/10.1023/A:1021221029301
MLA:
Neeb, Karl Hermann. "A Cartan–Hadamard Theorem for Banach–Finsler Manifolds." Geometriae Dedicata 95.1 (2002): 115-156.
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