Is there any relationship between the Lie ([itex]\pounds[/itex]) and covariant derivative ([itex]\nabla[/itex])?(adsbygoogle = window.adsbygoogle || []).push({});

Say I have 2 vector fields V, W and a metric g, the Lie and covariant derivative of W along V are:

[tex]\pounds_{V}W = [V,W][/tex]

[tex]V^\alpha \nabla_\alpha W^\mu = V^\alpha \partial_\alpha W^\mu + V^\alpha \Gamma^\mu_{\alpha \nu} W^\nu[/tex]

which appear rather different.

But conceptually I thought both derivatives help us to define what parallel transporting a vector in a general manifold means? Is there a good place to read about such issues?

Thanks!!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Lie vs. covariant derivative

Loading...

Similar Threads for covariant derivative |
---|

I Lie and Covariant derivatives |

A Commutator of covariant derivative and D/ds on vector fields |

A Interpretation of covariant derivative of a vector field |

I Covariant Derivative |

I Several covariant derivatives |

**Physics Forums | Science Articles, Homework Help, Discussion**