Conjugate and conformally conjugate parallelisms on Finsler manifolds |
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Authors: | Bernadett Aradi Mansoor Barzegari Akbar Tayebi |
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Institution: | 1.MTA-DE Research Group “Equations, Functions and Curves”, Hungarian Academy of Sciences and Institute of Mathematics,University of Debrecen,Debrecen,Hungary;2.Faculty of Science, Department of Mathematics,University of Qom,Qom,Iran |
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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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