Results 1 to 2 of 2

Thread: parametrization of torus

  1. #1
    Newbie
    Joined
    Jan 2015
    From
    england
    Posts
    1

    parametrization of torus

    Prove that the map F:Rm----->Cm given by F: (x1,...,xm)----->(eix1,...,eixe ) is a parametrization of the m-dimensional torus Tm in Cm​. Here C is stand for complex numbers. I have no idea really. Thank you for your helps.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,577
    Thanks
    1711

    Re: parametrization of torus

    Hey matholympicman.

    The torus is created by taking the unit circle [in the complex domain] and creating Cartesian products of all of them to get T^m.

    You have to show that by creating these Cartesian products you get the mapping listed above.

    Hint - Try looking at an inductive proof by showing that T^m X T = T^[m+1].
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Geodesics on a torus
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Nov 4th 2011, 05:22 PM
  2. Parametrization of the torus
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: Sep 5th 2011, 03:16 PM
  3. Area of a torus
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Dec 11th 2009, 07:40 PM
  4. torus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 2nd 2009, 07:32 AM
  5. Homology of the 3-Torus
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Mar 30th 2009, 03:32 AM

Search Tags


/mathhelpforum @mathhelpforum