对偶平坦Kropina度量（英文）
发布时间：2019-01-21 13:25
【摘要】：本文研究了一类具有奇性的芬斯勒度量——广义Kropina度量.文中给出了刻画广义Kropina度量的等价方程.进一步的研究工作表明,由共形1-形式β构造的Kropina度量是对偶平坦的,当且仅当其中的黎曼度量α是欧氏的,且该1-形式β是常向量场.还给出了一类很有意思的非平凡局部对偶平坦Kropina度量的例子.
[Abstract]:In this paper, we study a class of Fensler metric with singularity, generalized Kropina metric. In this paper, an equivalent equation characterizing the generalized Kropina metric is given. Further studies show that the Kropina metric constructed from conformal 1-form 尾 is dual flat if and only if the Riemannian metric 伪 is Euclidean and the 1-form 尾 is a constant vector field. An interesting class of nontrivial locally dual flat Kropina metrics is also given.
【作者单位】： 东南大学数学学院;后勤工程学院基础部;
【基金】：supported by NSFC(No.11371386) Frontier and Basic Research of Chongqing(No.cstc2014jcyjA00002) the Fundamental Research Funds for Central Universities(No.3207014403,No.3207014203)
【分类号】：O186.12
本文编号：2412704
[Abstract]:In this paper, we study a class of Fensler metric with singularity, generalized Kropina metric. In this paper, an equivalent equation characterizing the generalized Kropina metric is given. Further studies show that the Kropina metric constructed from conformal 1-form 尾 is dual flat if and only if the Riemannian metric 伪 is Euclidean and the 1-form 尾 is a constant vector field. An interesting class of nontrivial locally dual flat Kropina metrics is also given.
【作者单位】： 东南大学数学学院;后勤工程学院基础部;
【基金】：supported by NSFC(No.11371386) Frontier and Basic Research of Chongqing(No.cstc2014jcyjA00002) the Fundamental Research Funds for Central Universities(No.3207014403,No.3207014203)
【分类号】：O186.12
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1 黎芳,王佳;Kropina度量的一些射影性质及曲率性质[J];西南师范大学学报(自然科学版);2004年03期
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