The fundamental equations of a pseudo-Finsler submersion

TL;DR

This paper extends the fundamental equations of Riemannian submersions to pseudo-Finsler submersions, exploring properties of fundamental tensors and special cases with totally geodesic fibers.

Contribution

It generalizes classical submersion equations to the pseudo-Finsler setting and analyzes properties of associated tensors and special fiber conditions.

Findings

Generalized fundamental equations for pseudo-Finsler submersions

Analyzed properties of O'Neill fundamental tensors

Studied Finsler submersions with totally geodesic fibers

Abstract

The main result in this paper is the generalisation of the fundamental equations of a Riemannian submersion presented in the 1966 article by Barrett O'Neill to the context of pseudo-Finsler submersions. In the meantime, we also explore some basic properties of the O'Neill fundamental tensors of the submersion and study Finsler submersions with totally geodesic fibers.