# On Horizontal Recurrent Finsler Connections

## TL;DR

This paper explores horizontally recurrent Finsler connections using a pullback approach, establishing existence and uniqueness results, and introduces a special class called HRF-connections with specific properties.

## Contribution

It generalizes the Cartan connection theorem by proving existence and uniqueness of horizontally recurrent Finsler connections for any scalar 1-form.

## Key findings

- Existence and uniqueness of horizontally recurrent Finsler connections for any scalar 1-form
- Introduction and analysis of special HRF-connections with unique properties
- Extension of classical Finsler connection theory to recurrent cases

## 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.