List questions from connections

Published on 03 Feb 2023 - 22:43

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Derivation for expression for second covariant derivative

Published on 14 Feb 2023 - 22:12

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Definitions of Flat Connections

Published on 25 Mar 2026 - 15:46

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Details to Lie derivative of Christoffel symbols

Published on 26 Mar 2026 - 12:37

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How to identify parallel curves on a smooth manifold?

Published on 26 Feb 2023 - 10:38

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Riemann curvature tensor "as a" vector in the total space?

Published on 26 Mar 2026 - 12:41

69

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Connection with the second tangent bundle as a doamin

Published on 08 Mar 2023 - 17:02

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Induced connections

Published on 16 Mar 2023 - 6:08

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Metric induced by a linear combinations of inner products on a manifold

Published on 24 Mar 2023 - 22:55

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Definition of Covariant Derivatives Along Curves (John Lee, Theorem $4.24$)

Published on 25 Mar 2023 - 15:40

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Why does parallel transport along geodesics solve $\nabla_{r\partial_r}\tau=0$?

Published on 26 Mar 2023 - 8:41

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Bundle isomorphism and connection

Published on 01 Apr 2023 - 19:04

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"The curvature of $\nabla=\mathrm d+\omega$ equals $\mathrm{d}\omega+\omega\wedge\omega$"

Published on 02 Apr 2023 - 11:43

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Is the induced connection in the hom bundle compatible with the metric provided that the connections from which it comes are?

Published on 04 Apr 2023 - 19:36

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Proof that $L_X\omega=\iota_X(\mathrm{d}\omega+\omega\wedge\omega)$ if $\iota_X\omega=0$

Published on 26 Mar 2026 - 14:22

List Question

Use connection to give local trivialization of fibration

Derivation for expression for second covariant derivative

Definitions of Flat Connections

Details to Lie derivative of Christoffel symbols

How to identify parallel curves on a smooth manifold?

Riemann curvature tensor "as a" vector in the total space?

Connection with the second tangent bundle as a doamin

Induced connections

Metric induced by a linear combinations of inner products on a manifold

Definition of Covariant Derivatives Along Curves (John Lee, Theorem $4.24$)

Why does parallel transport along geodesics solve $\nabla_{r\partial_r}\tau=0$?

Bundle isomorphism and connection

"The curvature of $\nabla=\mathrm d+\omega$ equals $\mathrm{d}\omega+\omega\wedge\omega$"

Is the induced connection in the hom bundle compatible with the metric provided that the connections from which it comes are?

Proof that $L_X\omega=\iota_X(\mathrm{d}\omega+\omega\wedge\omega)$ if $\iota_X\omega=0$

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