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 at imagine fgf
) is a lower left corner of the rectangle and fgf
) is the upper right corner and x2
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
. 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 ?