On mean Cartan torsion of Finsler metrics

  • A. Dehghan Nezhad Department of Mathematics, Iran University of Science and Technology, Tehran
  • S. Beizavi School of Mathematics, Iran University of Science and Technology, Tehran
Keywords: Cartan torsion, generalized Randers metric, generalized $(a, b, J)$-metrics.

Abstract

UDC 514.7

We prove  that Finsler manifolds with unbounded mean Cartan torsion cannot be isometrically imbedded into any Minkowski space.  We also study the generalized Randers metrics obtained by the Rizza structure and show that any generalized Randers metric has an unbounded mean Cartan torsion. Then  generalized Randers metrics   cannot be isometrically imbedded into any Minkowski space. Further, we prove that every generalized Randers metric is quasi-C-reducible.  Finally, we show that every generalized Randers metric on 2-dimensional  Finsler manifold has a vanishing mean Cartan torsion.

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Published
11.04.2023
How to Cite
NezhadA. D., and BeizaviS. “On Mean Cartan Torsion of Finsler Metrics”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 3, Apr. 2023, pp. 337 -50, doi:10.37863/umzh.v75i3.6875.
Section
Research articles