Locally conformally Berwald manifolds and compact quotients of reducible manifolds by homotheties
Locally conformally Berwald manifolds and compact quotients of reducible manifolds by homotheties
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局部共形 Berwald 流形和拟似可约流形的紧商
DOI：
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发表时间：
2015
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通讯作者：
Y. Nikolayevsky
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作者：
V. Matveev;Y. Nikolayevsky
本文研究了局部共形Berwald度量在闭流形上的应用。我们证明了这样的度量的特征是等价于特征不完全的，单连通的，黎曼流形与可约holonomy群，其商由一组homotheties是封闭的。我们进一步证明了德拉姆型分裂定理，该定理指出，如果这样的流形是解析的，则它与欧几里得空间和不完全流形的黎曼积等距。
We study locally conformally Berwald metrics on closed manifolds which are not globally conformally Berwald. We prove that the characterization of such metrics is equivalent to characterizing incomplete, simply-connected, Riemannian manifolds with reducible holonomy group whose quotient by a group of homotheties is closed. We further prove a de Rham type splitting theorem which states that if such a manifold is analytic, it is isometric to the Riemannian product of a Euclidean space and an incomplete manifold.