Finsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature

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dc.creatorShen, Zhongmin
dc.date2003-11-14
dc.date.accessioned2026-07-07T05:02:53Z
dc.date.available2026-07-07T05:02:53Z
dc.descriptionThe flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an open subset in R^n with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler metric with negative flag curvature and constant S-curvature must be Riemannian if the manifold is compact. We also study the nonpositive flag curvature case.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0311232
dc.identifierhttp://arxiv.org/abs/math/0311232
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69189
dc.subjectDifferential Geometry
dc.subjectMetric Geometry
dc.subject53C60
dc.titleFinsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature
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