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Justification for taking derivatives through maps between manifolds

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#differential-geometry #smooth-manifolds #tangent-spaces
191
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Meaning of tangent space to $\mathbb{R}$

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#differential-geometry #vector-spaces #tangent-spaces
163
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Differential of a smooth covering map is always invertible?

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#smooth-manifolds #covering-spaces #tangent-spaces #pushforward
173
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Prove a subset is not a submanifold using dimension of the Tangent space

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#differential-geometry #smooth-manifolds #submanifold #tangent-spaces
110
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Orthonormal basis of the tangent space of a zero manifold

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#differential-geometry #manifolds #smooth-manifolds #orthonormal #tangent-spaces
70
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Projection of the tangent space of a zero manifold $M$ back onto $M$?

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#numerical-methods #manifolds #smooth-manifolds #karush-kuhn-tucker #tangent-spaces
21
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A special class of local charts of a zero manifold

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#differential-geometry #manifolds #smooth-manifolds #tangent-spaces
116
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How to establish the chart-independence of this equivalence relation on curves on a manifold

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#differential-geometry #smooth-manifolds #tangent-spaces
72
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Question about evaluating differential forms on (non)-basis vectors.

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#differential-geometry #smooth-manifolds #differential-forms #exterior-algebra #tangent-spaces
83
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Show that tangent plane of touching point is the same

Published on
#differential-geometry #tangent-spaces
55
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Combining derivatives of a composition of function

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#differential-geometry #tangent-spaces
78
Views

Why is the definition of the element $rv$ of the tangent space chart-independent?

Published on
#differential-geometry #smooth-manifolds #tangent-spaces
89
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tangent space of the manifold $\operatorname{Imm}(S^1,\mathbb{R}^d)$

Published on
#differential-geometry #submanifold #tangent-spaces
28
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Rank of Differential at penetration point

Published on
#differential-geometry #tangent-spaces
264
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Canonical orientation on a regular level set

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#differential-geometry #smooth-manifolds #vector-bundles #orientation #tangent-spaces

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