Answer to Question #351035 in Differential Geometry | Topology for Anna

Question

Let x(s) be a curve with arc length parametrization, and satisfies $||x(s)||\leq ||x(s_0)||\leq1$ for all s sufficiently close to x₀. Prove $\kappa$ (s₀) > 1. (Hint: Consider f(s) = ||x(s)|| ² . Then f(s) has a local maximum at s₀. Calculate f''(s₀))

Answer 1

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