Recent content by syra

Oh woops, I was being silly.

Excuse my laziness for not using latex. The coordinate transformation doesn't require an orthonormal set of v's, it just requires that ||v||=1/||N|| and orthogonality. The new coordinates require grad(X) = v = N/||N||^2, but we can lax this condition up by not requiring ||v||=1, in which case...

b(x) is a scalar-valued function, and N(x) a vector valued-function, taking on arguments in R^n. Not actually for schoolwork, but academic nonetheless.

Ah man, thanks Fredrik. When I first read this from Craig, I instantly thought it was something like the case with the Levi-Cevita connection: it's the unique torsion-free one, but this doesn't mean that which tangent vectors are parallel or not on a manifold is uniquely determined (i.e...

I had a much longer post typed with quotes and everything but I was auto-logged out, couldn't recover the text, and don't feel like typing it all in full. >:[ William Lane Craig, in "Einstein, Relativity, and Absolute Simultaneity" says that the Friedman metric as solution to Einstein's field...