• Support PF! Buy your school textbooks, materials and every day products Here!

Differential Geometry general question

  • #1
Ok, in general, I know that if the coefficients of the First Fundamental Form agree for two surfaces parameterized by X and Y, the the map X(Y^-1) is an isometry, or the two surfaces are isometric.

I also know that if two parameterizations don't have the same coefficients, this does not imply that the two surfaces are not isometric.

So i have two parameterizationsthat have different coefficients of the FFF (first fundamental form) but have the same Gaussian curvature. I need to prove that the two surfaces are not isometric. (ie i need to prove that the converse of Gauss's Great Theorem is false).
 

Answers and Replies

  • #2
bump bump any help?
 

Related Threads on Differential Geometry general question

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
0
Views
734
  • Last Post
Replies
4
Views
2K
Replies
2
Views
823
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
0
Views
691
  • Last Post
Replies
4
Views
2K
Top