Global theory of vertical recurrent Finsler connection
Commun. Korean Math. Soc. 2021 Vol. 36, No. 3, 593-607
https://doi.org/10.4134/CKMS.c200232
Published online June 11, 2021
Printed July 31, 2021
Amr Soleiman
Benha University
Abstract : The aim of the present paper is to establish an \emph{intrinsic} generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.
Keywords : Finsler manifold, Barthel connection, Cartan connection, Berwald connection, vertical recurrent Finsler connection
MSC numbers : Primary 53C60, 53B40, 58B20
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