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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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Immersion with respect to a connection?

In the paper hep-th/9712042v2, p. 20, the following setup is given: A complex manifold M and an n+1-dimensional vector bundle V on it. V has an underlying real bundle $V_{\mathbb{R}}$ with a flat con …
Thomas Trenner's user avatar