Increasing the dimensions of a manifold

  • B
  • Thread starter sqljunkey
  • Start date
  • #1
sqljunkey
175
7
Suppose I have a R^3 manifold that goes into R^3 charts, if that is possible. The manifold has curvature and is Riemannian and has a metric. I want to eliminate all curvature in R^3 charts, so I want to add another dimension to the manifold, I would extract all the curvature information from the manifold and deposit it into this new 4th dimension. I would probably also have to add some kind of topology or map to the new dimension describing the curvature. But I would have flat R^3 chart. Is this possible at all?
 

Answers and Replies

  • #2
andrewkirk
Science Advisor
Homework Helper
Insights Author
Gold Member
4,021
1,585
I'm not sure what your question is exactly, but the number of dimensions is a fundamental topological property of a manifold, so if we change the number of dimensions we have a different manifold.
 

Suggested for: Increasing the dimensions of a manifold

Replies
4
Views
197
Replies
2
Views
331
Replies
9
Views
2K
  • Last Post
Replies
5
Views
650
  • Last Post
Replies
20
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
7
Views
2K
Replies
4
Views
803
Replies
3
Views
2K
Replies
1
Views
727
Top