Consider a Riemannian metric in R^2, e.g. consider g given at a point (x,y) by the matrix(adsbygoogle = window.adsbygoogle || []).push({});

(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Surface with prescribed metric

**Physics Forums | Science Articles, Homework Help, Discussion**