Let \(\displaystyle \Sigma\) be a regular surface in \(\displaystyle \mathbb{R}^3\) with Gauss curvature larger than zero. Given any regular curve \(\displaystyle C\) contained in \(\displaystyle \Sigma\) and point \(\displaystyle p\) on \(\displaystyle C\), let \(\displaystyle k_1\) and \(\displaystyle k_2\) be the principal curvatures of \(\displaystyle \Sigma\) at \(\displaystyle p\) and \(\displaystyle \kappa(p)\) the curvature of \(\displaystyle C\) at \(\displaystyle p.\) Show that \(\displaystyle \kappa(p) \ge \text{min}\{|k_1|,|k_2|\}.\)
How will I solve this problem?
How will I solve this problem?
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