What is the Relationship Between Riemann Space and Relativity?

[m.medhat]

Homework Statement

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 ?

Homework Equations

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 .


Please I need help ….


Very thanks ……….

 

[George Jones]

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

 

[HallsofIvy]

Homework Statement

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 ?

Yes, that is really true.

Homework Equations

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 .

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?

Please I need help ….


Very thanks ……….

 

[m.medhat]

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

very thanks