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15
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Induced chart on tangent space

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#differential-geometry #riemannian-geometry #vector-bundles #tangent-spaces
84
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Lie Groups Homomrphism Question (Tangent Space)

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#abstract-algebra #differential-geometry #manifolds #lie-groups #tangent-spaces
69
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Why $\dim(\ker T_z f)=\dim(T_z(f^{-1}(c)))$?

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#manifolds #smooth-manifolds #submanifold #tangent-spaces
542
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“An Introduction to Manifolds”, Loring W.Tu, Example 8.19

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#general-topology #manifolds #smooth-manifolds #tangent-spaces
806
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Question on definition of time-orientability and future-directed curves

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#differential-geometry #curves #semi-riemannian-geometry #tangent-spaces
1.2k
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Tangent vector to a geodesic

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#differential-geometry #geodesic #semi-riemannian-geometry #tangent-spaces
69
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Tangent space of $O(n)$ by means of a composite of differential maps

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#proof-verification #manifolds #differential-topology #tangent-spaces
1.4k
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$T_pS \subseteq T_pM$: Are tangent spaces of submanifolds subsets (and not embedded) of tangent spaces of the original manifold?

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#geometry #differential-geometry #manifolds #smooth-manifolds #tangent-spaces
185
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Isn't this a trivial corollary?

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#derivatives #differential-geometry #orthogonality #submanifold #tangent-spaces
57
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Compact smooth manifolds where $M_1 \cap M_2$ is an infinte set

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#smooth-manifolds #tangent-spaces
135
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Does the unit tangent space of a point $p$ on the two-sphere, $S^2$ trace a unit circle?

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#differential-geometry #tangent-spaces
195
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Compact hypersurface

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#differential-geometry #riemannian-geometry #tangent-spaces
329
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From the definition of tangent space to the Lie algebra of a matrix group

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#differential-geometry #definition #lie-groups #lie-algebras #tangent-spaces
1.4k
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Differential of Multiplication Map of Lie Group

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#differential-geometry #manifolds #smooth-manifolds #tangent-spaces
53
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Will a velocity vector always generate the same curve under different charts?

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#differential-geometry #manifolds #tangent-spaces

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