# Riemann space and relativity

1. Aug 4, 2010

### m.medhat

1. The problem statement, all variables and given/known data
Hello ……..
I have a question about a statement mentioned in the book “Introduction to tensor calculus and continuum mechanics” . it is :-

Where the space (Vn) is Riemann space . Is this statement really true ?

2. Relevant equations

3. The attempt at a solution
… because - as I know – we can define a Non-Euclidean space (it isn’t flat) by this method , for example , we can do that in general theory of relativity .

Very thanks ……….

2. Aug 4, 2010

### George Jones

Staff Emeritus
Can you gives an example of a spacetime in general relativity that has this form?

3. Aug 4, 2010

### HallsofIvy

Yes, that is really true.

Can you give an example of a non-flat space in which the coeffients in the "first fundamental form", $ds^2= \epsilon_i (dx^i)^2$ are all either 1 or -1?

4. Aug 5, 2010

### m.medhat

thanks , when you said :- " are all either 1 or -1" , i understand .

very thanks