Recent content by mtiano

A solid sphere is not a surface. A surface is a 2D object. So it does not make sense to talk about things like the volume of a surface. When we talk about the 2D sphere, S^2, we mean the outer shell. Think of thing like hollow balls, hollow donuts, and deformed peices of paper. You can also have...

The set of all isometries on any riemannian manifold M forms a group called the isometry group on M. For R^n this is the set of all rigid motions each of which has the form f(x) = Ax + b where A is in O(n) and b is in R^n. For S^n this is the set of all orthagonal transformations, i.e. O(n). Now...

She retracted it after finding a mistake.

http://uoregon.edu/~koch/math433/Final.pdf

I'm not sure if this will help but I'll give it a try. It may depend on the configuration space you are using for relativity. For example one common configuration space is to take the space of all riemannian metrics on your manifold and mod out by the diffeomorphism group. Now if done this way...

Is it true that any smooth manifold admits a complete riemannian metric? Can you prove it? If not can you give a counter example? Obviously we can always put a riemannian metric on any smmoth manifold the question is does the differentable structure allow us to find a complete one.