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Results tagged with dg.differential-geometry
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user 332652
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
1
vote
1
answer
298
views
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 $\mathbb{A}$ …
CommunityBot
- 1
1
vote
Accepted
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 …
- 36