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

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Approximating the parallel transport map on a curve with the covariant derivative

Defining \begin{equation} \nabla_XY|_p := \lim_{t\to 0} \frac{\Pi_{tX}^{-1}(Y_{\phi^X(t)})-Y_p}{t} \end{equation} the approximation $\nabla_XY|_p \approx \frac{\Pi_{tX}^{-1}(Y_{\phi^X(t)})-Y_p}{t}$, f …
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1 vote
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Commutativity of tangent projection map and inner product

I stumbled into this simple property, that I can't find a proof of, although I verified it holds in a number of cases. Let $\mathbb{M}$ be a smooth manifold embedded into an ambient space $\mathbb{A}$ …
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