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Invariant Metrizability and Projective Metrizability on Lie Groups and Homogeneous Spaces

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Abstract

In this paper, we study the invariant metrizability and projective metrizability problems for the special case of the geodesic spray associated to the canonical connection of a Lie group. We prove that such canonical spray is projectively Finsler metrizable if and only if it is Riemann metrizable. This result means that this structure is rigid in the sense that considering left invariant metrics, the potentially much larger class of projective Finsler metrizable canonical sprays, corresponding to Lie groups, coincides with the class of Riemann metrizable canonical sprays. Generalisation of these results for geodesic orbit spaces are given.

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Authors and Affiliations

  1. Faculty of Mathematics, Alexandru Ioan Cuza University, Bulevardul Carol I 11, 700506, Iaşi, Romania

    Ioan Bucataru

  2. Institute of Mathematics, University of Debrecen, Egyetem tér 1, 4032, Debrecen, Hungary

    Tamás Milkovszki & Zoltán Muzsnay

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  1. Ioan Bucataru
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  2. Tamás Milkovszki
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  3. Zoltán Muzsnay
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Correspondence to Ioan Bucataru.

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Bucataru, I., Milkovszki, T. & Muzsnay, Z. Invariant Metrizability and Projective Metrizability on Lie Groups and Homogeneous Spaces. Mediterr. J. Math. 13, 4567–4580 (2016). https://doi.org/10.1007/s00009-016-0762-0

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  • DOI: https://doi.org/10.1007/s00009-016-0762-0

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