Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples). Modern differential geometry focuses "geometric structures" on such manifolds, such as bundles and connections; for questions not concerning such ...

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Studying the family of curves $\beta(s,r) = \alpha(s) + r\,{\bf N}(s)$

I'm reviewing some stuff on plane curves, just because, and I would like to confirm some things. The whole exercise is: Let $\alpha(s) = (x(s),y(s))$ be a unit-speed parametrized curve, ${\bf ...