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Gaussian curvature, mean curvature, sectional curvature, scalar curvature, curvature tensors (Riemann, Ricci, Weyl)
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Are there a geometry behind the singularity formation in solutions to nonlinear ODE's?
Indeed, I think, all is about the characteristics, and so, ultimately, about the Curvature... … In smooth category, curvature is in some sense (for me), just a formal way of identifying the normal form of a structure (in fact, the structure of the singularity, by taking a somewhat orthogonal angle …