# Finsler manifold

From Diffgeom

This article describes an additional structure on a differential manifold

View other additional structures

## Contents

## Definition

A **Finsler manifold** is the following data:

- A differential manifold
- A Banach norm on each tangent space such that the Banach norm is smooth as a function of position.

## Relation with other structures

### Stronger structures

- Riemannian manifold: Here the Banach norm is the usual norm associated with the inner product