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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

2 votes
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Prove that the trace of $\alpha$ is symmetric relative to the normal line of $\alpha$ at $0$

First, apologize for using $ \alpha $ and $ a $ together, then Let $a \in \mathbb{R}^+$, and let $\alpha : (-a, a) \rightarrow \mathbb{R}^2$ be a curve parameterized by arc length (p.b.a.l.) with $k_{ …