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 - The Fusion of Science and Community**

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 - covariant derivative | Date |
---|---|

A Commutator of covariant derivative and D/ds on vector fields | Thursday at 6:20 AM |

A Interpretation of covariant derivative of a vector field | Feb 15, 2018 |

I Covariant Derivative | Jan 16, 2018 |

I Several covariant derivatives | Aug 6, 2017 |

A Trying to understand covariant derivative on tensors | Jun 7, 2017 |

**Physics Forums - The Fusion of Science and Community**