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15
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Does the existence of the cross product relate to the triviality of $TS^n$?

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#differential-geometry #spheres #cross-product #tangent-bundle
97
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The map $f:T_1M\to \hat{\mathbb{R}}$ is continuous.

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#riemannian-geometry #tangent-bundle
30
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Differential of $(x,v)\mapsto (x,\exp_x(v))$

Published on
#geodesic #semi-riemannian-geometry #tangent-bundle
41
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What does the sentence "chart induces coordinates" really mean?

Published on
#differential-geometry #vector-bundles #tangent-bundle
23
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A question about the global representation of a tangent vector field.

Published on
#smooth-manifolds #vector-fields #tangent-bundle
387
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Charts and atlas for a tangent bundle (stereographic projection)

Published on
#differential-geometry #tangent-bundle #stereographic-projections
728
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Does every smooth local frame of the tangent bundle correspond to a chart?

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#differential-geometry #smooth-manifolds #vector-fields #tangent-bundle
65
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Calculating the tangent bundle of $O(m)$ and $SL(m)$.

Published on
#matrices #differential-geometry #tangent-bundle
314
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What are differential forms?

Published on
#vector-spaces #differential-topology #differential-forms #tangent-bundle #co-tangent-space
291
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Differential using sheaves

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#differential-geometry #differential-topology #smooth-manifolds #sheaf-theory #tangent-bundle
239
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Why do we use tangent bundles to define vector fields on manifolds?

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#differential-geometry #smooth-manifolds #vector-fields #tangent-bundle
537
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Show that there is a $\pi_i$-related smooth vector field for each smooth vector field $X_i \in \Gamma(M_i,TM_i)$

Published on
#differential-geometry #smooth-manifolds #vector-fields #tangent-bundle
189
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Jacobi field visualisation

Published on
#riemannian-geometry #tangent-bundle
207
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Pullback bundle, connections

Published on
#differential-geometry #smooth-manifolds #vector-bundles #semi-riemannian-geometry #tangent-bundle
85
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Definition of Wave map on manifolds

Published on
#differential-geometry #semi-riemannian-geometry #tangent-bundle #co-tangent-space

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