- #1
KarstenKarsten
- 3
- 0
Consider a Riemannian metric in R^2, e.g. consider g given at a point (x,y) by the matrix
(1 x
x 1+x^2 )
Is there a surface S, embedded in R^3, which has the property that the metric on S which is induced by the Euclidean metric of R^3 coincides with the given metric g? If yes, what representation does S possess?
(1 x
x 1+x^2 )
Is there a surface S, embedded in R^3, which has the property that the metric on S which is induced by the Euclidean metric of R^3 coincides with the given metric g? If yes, what representation does S possess?