Topology of curved space

  • Thread starter Niles
  • Start date
  • #1
1,868
0
[SOLVED] Topology of curved space

Homework Statement


The distance between a point (r, theta) and a nearby point (r + dr, theta + d\theta) on a positively curved sphere is given by

[tex]
ds^2 = dr^2 + R^2 \sin ^2 (r/R)d\theta ^2
[/tex]

NOTE: I mean that ds^2 = (ds^2). My question is - how do I use this formula? What is what - can you explain it to me?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
969
I'm not sure what your question is. You titled this "Topology of curved space" but topology does not concern itself with distances. You give a formula that involves R but don't say what R is. Apparently your "positively curved sphere" is a sphere of radius R. And if that is the case, then what are your coordinates? In particular, what is "r"?
 
  • #3
1,868
0
We are dealing with cylindrical coordinates.

So ds is the distance between points (r, theta) and (r+dr, theta + d theta).

Yes, R is the radius of the sphere - I'm sorry I did not mention that earlier.
 

Related Threads on Topology of curved space

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
12
Views
4K
  • Last Post
Replies
3
Views
864
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
1
Views
1K
Replies
4
Views
1K
Top