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Holonomy bundle is a covering space

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#differential-geometry #lie-groups #lie-algebras #connections #principal-bundles
217
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How to show that extension of linear connection commutes with contraction.

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#riemannian-geometry #tensors #trace #connections
2.5k
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Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold

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#differential-geometry #manifolds #riemannian-geometry #connections
623
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Conectionless parallel transport

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#differential-geometry #connections
458
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Holonomy group and irreducible $\mathrm{SU}(2)$-connections

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#differential-geometry #connections #principal-bundles #gauge-theory #holonomy
4.7k
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How is the covariant derivative of a metric, $\nabla g$, defined?

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#differential-geometry #riemannian-geometry #connections
762
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Different definitions of irreducible $\mathrm{SU}(2)$ connections

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#differential-geometry #connections #principal-bundles #gauge-theory
135
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If $\nabla X=h \cdot \text{Id}_{TM}$ for a vector field $X$ and $h \in C^{\infty}(M)$, is $h$ constant?

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#riemannian-geometry #vector-fields #connections
829
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Connection on a vector bundle in terms of sections

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#differential-geometry #vector-bundles #connections
160
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Passage in the proof of Chern-Weil method in John Roe's Elliptic operators book

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#differential-geometry #connections #characteristic-classes
67
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Proving that a form is horizontal in the Chern Weil method proof

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#differential-geometry #connections #characteristic-classes #principal-bundles
561
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A flow of a parallel vector field preserves the connection?

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#differential-geometry #riemannian-geometry #calculus-of-variations #vector-bundles #connections
176
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There is a natrual connection on the tangent bundle?

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#geometry #differential-geometry #connections #big-picture
430
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Defining connection from parallel transport

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#differential-geometry #connections
903
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Frobenius theorem to prove that flat connection admits a local basis of flat sections

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#differential-geometry #vector-bundles #connections

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