Communications of the
Korean Mathematical Society CKMS

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