Conjugate and conformally conjugate parallelisms on Finsler manifolds

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• 作者：Bernadett Aradi ; Mansoor Barzegari ; Akbar Tayebi
• 关键词：Conjugate parallelisms ; Conformal change ; Generalized Berwald manifold ; Wagner manifold ; Berwald manifold ; Lie group
• 刊名：Periodica Mathematica Hungarica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：74
• 期：1
• 页码：22-30
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1588-2829
• 卷排序：74

文摘

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.