Recent content by v2536

yes. that make sense. Now i got the solution, thanks for your help.

ok i think i understand now, if i use orthonormal basis then the connection may no be Levis-Civita.

Thank you chiro and Ben for your reply :) I see that i forgot about \sqrt{g} in front but can't i always find an orthonormal basis and work in that? and by doing that g should become 1 right?

What you have to calculate is the length of paths which are all geometric object. So no matter how to parametrize them (pick out vector in this case) the integral will give you the same result (the length). And if you use the fact that given two points A and B you can find the parametrization of...

Homework Statement Using the definition of divergence d(i_{X}dV) = (div X)dV where X:M\rightarrow TM is a vector field, dV is a volume element and i_X is a contraction operator e.g. i_{X}T = X^{k}T^{i_{1}...i_{r}}_{kj_{2}...j_{s}}, prove that if we use Levi-Civita connection then the...