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Geodesic equation

  1. Apr 23, 2012 #1
    http://mykomica.org/boards/shieiuping/physics/src/1335180831965.jpg [Broken]
    http://mykomica.org/boards/shieiuping/physics/src/1335180965708.jpg [Broken]
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Apr 23, 2012 #2
    The bigger words is the main description.
    The smaller words is my own work,
    I don't know if I get the wrong Christoffel connections or something else.
  4. Apr 28, 2012 #3


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    The Lie bracket of the two unit vector fields, (1 + z[itex]\bar{z}[/itex])[itex]\partial[/itex]x

    and (1 + z[itex]\bar{z}[/itex])[itex]\partial[/itex]y

    is orthogonal to (1 + z[itex]\bar{z}[/itex])[itex]\partial[/itex]x
    along the x axis and so is tangent to a geodesic.

    Now use the symmetry of the metric to solve the general case.
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