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Math Help - Greatest convex geodesic ball in Grassmannian

  1. #1
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    Greatest convex geodesic ball in Grassmannian

    Hello,

    Ive got a question concerning convex balls:

    Let 0<k<n and G(n,k) denote the Grassmannian of (non-oriented) k-planes in \IR^n. If P is a k-plane in G(n,k), what is the greatest radius r>0, such that the geodesic ball
    B_r(P) is convex?

    Thank you for helping me!
    Regards,
    Kevin
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  2. #2
    Super Member Rebesques's Avatar
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    Consider all radial geodesics g eminating from P. Then, the infimum of injectivity radii m over the set \{g\} is attained, as G(n,k) is compact. Maybe you will be required to additionaly show the ball B(m) is convex,
    a fact I find reasonable... but can't produce a formal proof at the moment. :P


    ps. disregard that. it's fairly simple
    Last edited by Rebesques; January 3rd 2011 at 12:03 PM.
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