期刊
JOURNAL OF GEOMETRIC ANALYSIS
卷 30, 期 1, 页码 617-631出版社
SPRINGER
DOI: 10.1007/s12220-019-00158-7
关键词
Finsler metrics; Constant flag curvature; Weyl-type curvature; Beltrami Theorem
类别
资金
- Ministry of Research and Innovation within Program 1-Development of the national RD system, Subprogram 1.2- Institutional Performance-RDI excellence funding projects [34PFE/19.10.2018]
We define a Weyl-type curvature tensor that provides a characterisation for Finsler metrics of constant flag curvature. When the Finsler metric reduces to a Riemannian metric, the Weyl-type curvature tensor reduces to the classical projective Weyl tensor. In the general case, the Weyl-type curvature tensor differs from the Weyl projective curvature, it is not a projective invariant, and hence Beltrami Theorem does not work in Finsler geometry. We provide the relation between the Weyl-type curvature tensors of two projectively related Finsler metrics. Using this formula we show that a projective deformation preserves the property of having constant flag curvature if and only if the projective factor is a Hamel function. This way we provide a Finslerian version of Beltrami Theorem.
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