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Results tagged with connections
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user 5659
Ehresmann connections; covariant derivatives; connections on vector bundles, principal bundles, ∞-bundles, submersions, bundle gerbes; holonomy and higher holonomy; parallel transport; torsion; curvature. See also the tags [principal-bundles], [vector-bundles], [gerbes], [curvature], [geodesics], [characteristic-classes], [torsion].
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Existence of a connection $A$ on a holomorphic line bundle $L$, s.t $F(A)=(\deg L)\omega$
Let $h_0$ be any hermitian metric on $L$, with curvature $F(h_0)$.
By Hodge theory, there exists a function $f\in \mathcal C^{\infty}(X)$ such that
$$\Delta_{\omega} f =\Lambda_{\omega} F(h_0) - \ma …
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