Integral curvature bounds and diameter estimates on Finsler manifolds
نویسندگان
چکیده
منابع مشابه
On Stretch curvature of Finsler manifolds
In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied. In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...
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The 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) nonRiemannian Finsler metrics on an open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler met...
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In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n ≥ 3. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat.
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This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. The first remark is that there is a canonical Kähler structure on the space of geodesics of such a manifold. The second remark is that there is a natural way to construct a (not necessarily complete) Finsler n-manifold of constant positive flag curvature out ...
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Seiberg-Witten theory leads to a remarkable family of curvature estimates governing the Riemannian geometry of compact 4-manifolds, and these, for example, imply interesting results concerning the existence and/or uniqueness of Einstein metrics on such spaces. The primary purpose of the present article is to introduce a simplified, user-friendly repackaging of the information conveyed by the Se...
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ژورنال
عنوان ژورنال: Science China Mathematics
سال: 2019
ISSN: 1674-7283,1869-1862
DOI: 10.1007/s11425-018-9459-1