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Is there a way to define a submanifold of a Euclidean space by providing a list of implicit constraints, instead of by declaring a separate manifold and explicitly defining the embedding?

Reasons for asking: My ultimate goal is to be able to integrate vector and form fields on surfaces defined by constraints in a 3D Euclidean space. A simple example would be the sphere (x^2 + y^2 + z^2 = R^2).