Abstract
This paper considers fundamental issues related to Finslerian isometries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Using distance coordinates, a simple proof is given for the Finslerian version of the Myers–Steenrod theorem and for the differentiability of Finslerian submetries.
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Dedicated to Professor Lajos Tamássy on the occasion of his 90th birthday
The first author’s research was supported by the Hungarian Academy of Sciences. Both authors were supported by the TÁMOP-4.2.2/B-10/1-2010-0024 project and the TÁMOP 4.2.4. A/2-11-1-2012-0001 “National Excellence Program – Elaborating and operating an inland student and researcher personal support system convergence program”. The project is co-financed by the European Union and the European Social Fund.
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Aradi, B., Kertész, D.C. Isometries, submetries and distance coordinates on Finsler manifolds. Acta Math. Hungar. 143, 337–350 (2014). https://doi.org/10.1007/s10474-013-0381-1
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DOI: https://doi.org/10.1007/s10474-013-0381-1