# nLab Killing spinor

### Context

#### Riemannian geometry

Riemannian geometry

## Applications

#### Differential geometry

differential geometry

synthetic differential geometry

# Contents

## Idea

A Killing spinor on a (pseudo-)Riemannian manifold is a covariantly constant spinor : a section of some spinor bundle $v \in \Gamma(S)$ that is annihilated by the covariant derivative of the corresponding Levi-Civita connection.

Similarly a Killing vector is a covariantly constant vector field.

## References

A discussion with an eye towards applications in supersymmetry is around page 907 in volume II of

Revised on November 14, 2013 21:34:18 by Urs Schreiber (82.169.114.243)