I have a question about connections derived from degenerate metrics, like in Newton-Cartan.(adsbygoogle = window.adsbygoogle || []).push({});

The question is simply: can the transformation properties of the connection change if one considers connections derived from metrics which are degenerate?

One one hand, I would say that one can follow the usual GR-analysis, check how covariant derivatives of general vectors/covectors must transform and conclude how the connection must transform (with a inhomogeneous term).

On the other hand, in Newton-Cartan one has the metric conditions

[tex]

\nabla_{\mu}\tau_{\nu} = 0, \ \ \ \ \nabla_{\rho}h^{\mu\nu}=0

[/tex]

where [itex]h^{\mu\nu}\tau_{\nu}=0[/itex]; h plays the role of spatial metric, and tau the role of temporal metric.

So, do the transformation properties of the connection depend on the metrical structure?

**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!

# Connections of degenerate metrics

Loading...

Similar Threads - Connections degenerate metrics | Date |
---|---|

I Connections on principal bundles | Jan 22, 2018 |

A Is the Berry connection a Levi-Civita connection? | Jan 1, 2018 |

A Can you give an example of a non-Levi Civita connection? | Oct 30, 2017 |

I Arbitrariness of connection and arrow on sphere | Aug 14, 2017 |

Is a cone the degenerate of a 4 dimensional hyperbola? | Jan 30, 2013 |

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