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center o bass
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A regular curve on a manifold ##M## is a curve ##\gamma:I \to M## such that ##\dot \gamma(t) \neq 0## for any ##t \in I##. In John Lee's "Introduction to Curvature" he says that this intuitively means that we prevent the curve from having "cusps" and "kinks".
How can I see that this is the case? I.e. how could ##\dot \gamma(t) = 0## for some t lead to a "kink" or "cusp"?
How can I see that this is the case? I.e. how could ##\dot \gamma(t) = 0## for some t lead to a "kink" or "cusp"?