Results 1 to 2 of 2

Math Help - stereographic projection, again

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    38

    stereographic projection, again

    The problem:
    Let \phi:\mathbb{R}^3 \rightarrow S^3 be the inverse of stereographic projection from S^3-\{(0, 0, 0, 1)\} to the equatorial hiperplane x_4=0. Show that for every vector p \in \mathbb{R}^3 exists \lambda(p) \in \mathbb{R}^3 such that
    ||d\phi(\textbf{v})||= \lambda (p) ||\textbf{v}||, \forall \textbf{v} \in {\mathbb{R}^3}_p.

    The solution must rely on the following hint: the vector part of d \phi (\textbf{v}) is (d/dt)|_{t=0} \phi (p + tv), where \textbf{v}=(p, v).

    I can't even get this vector part right..

    As always, thanks for all the hints and help.
    I will continue to work on it and post if I get anything.

    (If it matters, it's not homework or exam question, just exercise.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jun 2008
    Posts
    38
    I managed to get the vector part right.
    But how do I use the hint?

    If someone has the time, I'd really appreciate it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex Analysis - Stereographic Projection
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 15th 2011, 01:01 AM
  2. Cross ratios, inversions and stereographic projections
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 21st 2010, 02:20 PM
  3. Replies: 1
    Last Post: December 2nd 2009, 10:14 PM
  4. Projection map
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 12th 2009, 09:28 AM
  5. Projection
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 18th 2009, 01:42 PM

Search Tags


/mathhelpforum @mathhelpforum