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Conjugate and conformally conjugate parallelisms on Finsler manifolds

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Abstract

In this paper we study conjugate parallelisms and their conformal changes on Finsler manifolds. We provide sufficient conditions for a Finsler manifold endowed with two conjugate (resp. conformally conjugate) covering parallelisms to become a Berwald (resp. Wagner) manifold. As an application for Lie groups, we give a new proof for a theorem of Latifi and Razavi about bi-invariant Finsler functions being Berwald. By introducing the concept of a conformal change of a parallelism, we also obtain a conceptual proof of a theorem of Hashiguchi and Ichijyō: the class of generalized Berwald manifolds is closed under conformal change.

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Acknowledgments

The authors are grateful to József Szilasi, supervisor of the first author, for his valuable comments and suggestions. They thank Balázs Csikós for suggesting a significant simplification of the original proof of Theorem 3.3. The first author’s research was supported by the Hungarian Academy of Sciences.

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Correspondence to Bernadett Aradi.

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Aradi, B., Barzegari, M. & Tayebi, A. Conjugate and conformally conjugate parallelisms on Finsler manifolds. Period Math Hung 74, 22–30 (2017). https://doi.org/10.1007/s10998-016-0152-1

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