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Extending a vector field to a ball

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#manifolds #riemannian-geometry #smooth-manifolds #vector-fields #connections
61
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Torsion of particular form

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#differential-geometry #connections
1.7k
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Prove that the Christoffel symbols vanish in $\mathbb{R}^n$

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Covariant derivative of tensor densities

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#differential-geometry #tensors #connections
517
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Levi-Civita Connection Example of a calculation

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#differential-geometry #riemannian-geometry #smooth-manifolds #connections
645
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Push-forward of Levi-Civita connection.

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#differential-geometry #manifolds #riemannian-geometry #smooth-manifolds #connections
644
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Uniqueness of induced covariant derivatives of tensor fields

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40
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Existence of connection with full holonomy

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#differential-geometry #differential-topology #connections
239
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Heat kernel, connection on fibre bundles: reference request

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#differential-geometry #reference-request #fiber-bundles #connections
1.5k
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The First Partial Derivatives of Metric Coefficients in Normal Coordinates Vanish at the Center

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#differential-geometry #riemannian-geometry #connections
1.4k
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Parallel transport around a closed loop

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#differential-geometry #riemannian-geometry #tensors #curvature #connections
213
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Are Riemannian submersions affine?

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#riemannian-geometry #vector-bundles #connections
1.7k
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Lie derivative characterisation of the Levi-Civita connection

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#differential-geometry #riemannian-geometry #connections #lie-derivative
560
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Vertical and horizontal subspace , simple and concrete example.

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#differential-geometry #fiber-bundles #connections #principal-bundles
348
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Connection with examples

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#differential-geometry #connections

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