Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Rebesques

Thread: non-euclidean metric on 2-sphere??

  1. #1
    Fat
    Fat is offline
    Newbie
    Joined
    Jan 2015
    From
    MOROCCO
    Posts
    2

    Question non-euclidean metric on 2-sphere??

    Hi,
    In the context of calculating the metrics, the 2-sphere is often equipped with the Euclidean metric (identity matrix),
    is it always correct?
    can we equip the 2-sphere with a NON-Euclidean metric?

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Rebesques's Avatar
    Joined
    Jul 2005
    From
    My house.
    Posts
    658
    Thanks
    42

    Re: non-euclidean metric on 2-sphere??

    I think you have answered your own question, by stating that the matrix should not have to be the identity. Any positive definite matrix will do.

    Other than that, there is another metric you can define on the 2-sphere that does not depend on ambient space. You can define the distance between
    any two points as the length of the shortest geodesic with these as endpoints.
    Last edited by Rebesques; Jan 18th 2015 at 11:50 AM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Fat
    Fat is offline
    Newbie
    Joined
    Jan 2015
    From
    MOROCCO
    Posts
    2

    Re: non-euclidean metric on 2-sphere??

    Thank you for your helpful response , I found that the shortest geodesic between two points X and Y on the 2-sphere is the distance d=arcos(X'.Y),

    I dont know how find the matrix form of this distance !! because I wiil need it for computing the pullback metric..;
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Euclidean metric vs Taxicab metric?
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Feb 25th 2013, 12:25 PM
  2. Replies: 0
    Last Post: Sep 17th 2011, 03:44 PM
  3. [SOLVED] Euclidean metric is a metric
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Jan 14th 2011, 12:13 AM
  4. Show that the Euclidean plane is a metric space?
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: Apr 27th 2010, 04:42 AM
  5. Sets > Metric Space > Euclidean Space
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Apr 25th 2010, 10:17 PM

Search Tags


/mathhelpforum @mathhelpforum