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Hello. So, we have curves and surfaces. We already know about generally manifolds and Riemannian manifolds but what i want to produce are ways to abstract curves or surfaces but i am not talking about manifolds. Do you have any ideas? Perhaps the feature of curvature would help? To make an abstraction of curvature and define the corresponding objects? We know about the Gaussian curvature, so how would someone abstract it? Thank you.