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Finding the geodesic function for scalar * function= scalar

  1. Jul 27, 2012 #1
    56baaad965b3374c53c31863fac4d60e.png



    In this expression the junk on the left is a scalar. The stuff before the integral is another scalar. The integral is a time-like curve between x1 and x2 and at imagine fgf(x1) is a lower left corner of the rectangle and fgf(x2) is the upper right corner and x2-x1 is the length of the base of the rectangle. I know the geodesic is the shortest distance curve paramaerized by this on the condition that the area (the integral) times the scalar1 = scalar2. The solution isn't a strait line but could be some curved function. How do I find the function fgf ?



    Do i need to find the 2x2 metric tensor for the 2-d paramaterization curve and solve a pair of differential equations like here ?

    http://count.ucsc.edu/~rmont/classes/121A/polarChristoffelE_Lag.pdf
     
  2. jcsd
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