Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

Perhaps I'm asking the wrong question but I am wondering about the relationship between different definitions of, for the sake of argument, the torus.

We can define it parametrically (or as a single constraint) and from there work out the induced metric as with any surface.

But we can also define it by considering the plane and identifying opposite sides. Is it possible to use this definition, equip the plane with Cartesian coordinates and then deduce the metric on the torus caused by the identification?

I hope I've explained myself and apologise if it's an ill-thought-out question.

Thanks,

I

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

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!

# Metric on torus induced by identification of points on plane

Loading...

Similar Threads for Metric torus induced |
---|

I Surface Metric Computation |

I Metrics and topologies |

I Lie derivative of a metric determinant |

I Conformal Related metrics |

A On the dependence of the curvature tensor on the metric |

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