On horizontal recurrent Finsler connections

Abstract

In this paper we adopt the pullback approach to global Finsler geometry. We investigate horizontally recurrent Finsler connections. We prove that for each scalar ( $$\pi $$ )1-form A, there exists a unique horizontally recurrent Finsler connection whose h-recurrence form is A. This result generalizes the existence and uniqueness theorem of Cartan connection. We then study some properties of a special kind of horizontally recurrent Finsler connection, which we call special HRF-connection.