Projectively flat Finsler manifolds with infinite dimensional holonomy
Projectively flat Finsler manifolds with infinite dimensional holonomy
复制标题
具有无限维完整的投影平坦芬斯勒流形
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
P. Nagy
中科院分区：
文献类型：
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作者：
Z. Muzsnay;P. Nagy
最近，我们提出了一种研究非黎曼Finsler流形完整性的方法，得到了如果维数$ bbbb2 $的Finsler流形具有非零的常标志曲率，那么完整群不可能是紧李群。本文的目的是进一步探讨非零常旗曲率的射影平面Finsler流形的完整性。特别证明了非零常旗曲率的射影平坦Randers流形和Bryant-Shen流形具有无限维完整群。
Recently, we developed a method for the study of holonomy properties of non-Riemannian Finsler manifolds and obtained that the holonomy group can not be a compact Lie group, if the Finsler manifold of dimension $> 2$ has non-zero constant flag curvature. The purpose of this paper is to move further, exploring the holonomy properties of projectively flat Finsler manifolds of non-zero constant flag curvature. We prove in particular that projectively flat Randers and Bryant-Shen manifolds of non-zero constant flag curvature have infinite dimensional holonomy group.