# nLab Weitzenböck connection

### Context

#### Riemannian geometry

Riemannian geometry

## Applications

#### Differential geometry

differential geometry

synthetic differential geometry

## Applications

On a (pseudo)Riemannian manifold the Weitzenböck connection is the affine connection on the tangent bundle which has vanishing curvature but possibly non-vanishing torsion.

This is in contrast to the Levi-Civita connection, for which it is the other way around.

Created on April 21, 2012 09:52:57 by Urs Schreiber (82.113.119.35)