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arXiv · 1808.05001

A characterisation for Finsler metrics of constant curvature and a Finslerian version of Beltrami Theorem

Ioan Bucataru·Georgeta Creţu
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Abstract

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 classic 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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Ioan Bucataru, Georgeta Creţu. 2018-08-17. A characterisation for Finsler metrics of constant curvature and a Finslerian version of Beltrami Theorem. https://doi.org/10.1007/s12220-019-00158-7

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