Isometric embedding of two dimensional Riemannian manifolds

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A two dimensional Riemannian manifold is an abstract surface sitting nowhere in particular, but which somehow has the structures imposed on it that a surface gets by sitting in Euclidean space, such as tangent spaces, a metric etc.

The question is whether such an abstract surface can be realized as a surface in three dimensional Euclidean space. This problem can be reduced to solving a certain Monge-Ampere equation.

Updated:  21 January 2018/Responsible Officer:  Director/Page Contact:  School Manager