# Torsion of a linear connection

From Diffgeom

*This article defines a tensor (viz a section on a tensor bundle over the manifold) of type* (1,2)

## Definition

### Given data

- A differential manifold
- A linear connection on (viz., a connection on the tangent bundle ).

### Definition part

The torsion of , denoted as , is defined as a map that takes as input 2 vector fields and outputs a third vector field, as follows:

A linear connection whose torsion is zero is termed a **torsion-free linear connection**.

### Tensoriality

`Further information: Torsion is tensorial`
The torsion map is a tensor. It is tensorial in both and .