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15
64
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Connections and curvature on line bundles

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#differential-geometry #curvature #connections #line-bundles
75
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Affine connection on non smooth vector fields

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#differential-geometry #vector-fields #connections
90
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Invariant differential forms?

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#differential-geometry #algebraic-topology #connections #principal-bundles #gauge-theory
54
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Understanding the Cartan connection in the context of General Relativistic spacetime.

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#differential-geometry #mathematical-physics #fiber-bundles #connections
207
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Why does the adjoint representation appear in the definition of a connection 1-form?

Published on
#differential-geometry #smooth-manifolds #connections #principal-bundles #gauge-theory
101
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Motivation for Connections over smooth manifolds

Published on
#derivatives #differential-geometry #euclidean-geometry #vector-bundles #connections
34
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Tensor change of coordinates - why one way is inverse matrix of the other?

Published on
#differential-geometry #connections
532
Views

Intuition behind connection 1-forms and Ehresmann connections

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#differential-geometry #fiber-bundles #connections #principal-bundles #gauge-theory
148
Views

Connection Leibniz rule

Published on
#riemannian-geometry #vector-bundles #connections
50
Views

A connection along a curve is $C^{\infty}(I)$-linear.

Published on
#differential-geometry #riemannian-geometry #connections
95
Views

Coordinatefree Cartan-Maurer

Published on
#differential-geometry #connections
48
Views

How does $\partial_\mu$ act on $A_\nu$ in the local structure equation for a curvature 2-form written in coordinates?

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#differential-geometry #lie-algebras #curvature #connections #principal-bundles
35
Views

How to determine the notion of parallel transport within the conformal or projective and general connections?

Published on
#geometry #differential-geometry #connections
80
Views

Local expression of covariant derivative on associated vector bundle

Published on
#differential-geometry #connections #principal-bundles
89
Views

Affine connections: alternatives to the Levi-Civita connection

Published on
#differential-geometry #connections

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