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## Main Question or Discussion Point

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?