On mean Cartan torsion of Finsler metrics

A. Dehghan  Nezhad; S.  Beizavi

doi:10.37863/umzh.v75i3.6875

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

DOI: https://doi.org/10.37863/umzh.v75i3.6875

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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