List questions from connections

Published on 25 Mar 2026 - 12:55

119

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Why is $\Pi(X,Y)=\frac{\partial}{\partial t} \nabla_XY$?

Published on 19 Mar 2026 - 12:41

67

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Defining a connection in $\mathbb{R}^2$ using a connection $1$-form

Published on 25 Mar 2026 - 1:34

444

Views

Connection on the dual vector bundle

Published on 18 Oct 2018 - 12:19

162

Views

Isn't $∇^{0,1}=\bar\partial_E+A^{0,1}$?

Published on 18 Oct 2018 - 20:03

367

Views

Connection on the cotangent bundle

Published on 22 Oct 2018 - 19:30

69

Views

Upper bound on distance between trajectories that share same initial position and velocity

Published on 25 Mar 2026 - 6:27

118

Views

a torsion-free connection that preserves a complex structure

Published on 30 Oct 2018 - 17:04

405

Views

How to look at the covariant derivative along a curve?

Published on 08 Nov 2018 - 15:08

521

Views

Uniqueness of horizontal lifts

Published on 25 Mar 2026 - 12:53

121

Views

When (if ever) does a connection on a Lie manifold G define that groups Lie algebra?

Published on 19 Nov 2018 - 9:18

214

Views

Show that any affine connection $\nabla$ on $\mathbb{R}^n$ is of the form $\nabla=D+\Gamma$.

Published on 21 Nov 2018 - 21:49

157

Views

Torsion-freeness of a connection and anti-symmetrization

Published on 24 Nov 2018 - 12:10

149

Views

Different almost-complex structures $\Rightarrow$ different complex structures?

Published on 26 Nov 2018 - 18:03

508

Views

Levi-Civita connection for a metric in $\mathbb{R}^{3}$

Published on 25 Mar 2026 - 8:09

List Question

Covariant derivative vs. Ehresmann connection

Why is $\Pi(X,Y)=\frac{\partial}{\partial t} \nabla_XY$?

Defining a connection in $\mathbb{R}^2$ using a connection $1$-form

Connection on the dual vector bundle

Isn't $∇^{0,1}=\bar\partial_E+A^{0,1}$?

Connection on the cotangent bundle

Upper bound on distance between trajectories that share same initial position and velocity

a torsion-free connection that preserves a complex structure

How to look at the covariant derivative along a curve?

Uniqueness of horizontal lifts

When (if ever) does a connection on a Lie manifold G define that groups Lie algebra?

Show that any affine connection $\nabla$ on $\mathbb{R}^n$ is of the form $\nabla=D+\Gamma$.

Torsion-freeness of a connection and anti-symmetrization

Different almost-complex structures $\Rightarrow$ different complex structures?

Levi-Civita connection for a metric in $\mathbb{R}^{3}$

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