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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
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Two ways to differentiate a section of vector bundle
Let $\pi:E\rightarrow M$ be a vector bundle, and $D$ a connection on it. Suppose $\sigma_1,\sigma_2\in\Gamma(E)$, $p\in M$, $V\in T_pM$ such that $\sigma_1(p)=\sigma_2(p)$. Are the following two condi …