Hello.(adsbygoogle = window.adsbygoogle || []).push({});

Let M,N be a connected smooth riemannian manifolds.

I define the metric as usuall, the infimum of lengths of curves between the two points.

(the length is defined by the integral of the norm of the velocity vector of the curve).

Suppose phi is a homeomorphism which is a metric isometry.

I wish to prove phi is a diffeomorphism.

Please, anyone who can help.

Thanks in advance,

Roey

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

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!

# Riemannian Geometry

Loading...

Similar Threads - Riemannian Geometry | Date |
---|---|

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

I Lie derivative of a metric determinant | Dec 22, 2017 |

A On the dependence of the curvature tensor on the metric | Nov 2, 2017 |

A Pushforward map | Sep 24, 2017 |

A Geometrical interpretation of Ricci and Riemann tensors? | Jul 15, 2016 |

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