Finsler functions consistent with absolute parallelisms

摘要

In this note we generalize a result of J.A. Wolf on Riemannian metrics consistent with absolute parallelisms to the Finslerian case. Along the way we obtain necessary and sufficient conditions for a parallelizable manifold to become a Lie group whose left parallelism is induced by the given one. It also turns out that a Finsler function consistent with an absolute parallelism is necessarily of Berwald type. (C) 2017 Elsevier B.V. All rights reserved.