The failure of "parallel transport around a closed loop" to be the identity map. Studied in differential geometry, it is intimately tied with curvature.
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Holonomy of the sphere
I saw an example in which the holonomy of $\mathbb{S}^n$ with the standard metric is calculated. I'm just starting to get familiar with holonomy groups and I wanted to know what could one do by ...
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How does the holonomy act on the tangent space at a point?
Suppose $(X,h)$ is a compact $n$-dimensional Hermitian manifold, with holonomy group $H$. Now we know,since $X$ is a complex manifold, that $H\subset U(n)$, and that there is a representation of $H$ ...
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Holonomy group of quotient manifold
Let $(M,g_M)$ be a compact Riemannian manifold with holonomy group $Hol(M,g_M)$. Suppose that a finite group $G$ acts on $M$ freely and preserves the metric $g$.
What can one say about the holonomy ...
