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Gaussian curvature, mean curvature, sectional curvature, scalar curvature, curvature tensors (Riemann, Ricci, Weyl)

3 votes

Necessary and sufficient curvature condition for a regular planar curve to be simple and closed

The Four-vertex theorem dictates that the curvature function needs to have at least two local minima and maxima. … For arbitrary curvature functions satisfying the Four-vertex condition and a fixed parametrization, I don't believe it is possible to answer the question. …
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