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Application of the Poincare lemma from Spivak

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#calculus #real-analysis #differential-geometry #manifolds #smooth-manifolds
99
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Computing the pullback of $-\frac{y}{x^2+y^2}dx+\frac{x}{x^2+y^2}dy$

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#calculus #real-analysis #differential-geometry #manifolds #differential-forms
188
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Lie group SU(n) and symmetric group S$_k$

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#abstract-algebra #finite-groups #manifolds #lie-groups #lie-algebras
83
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On the flow of $v(x,y)=(x,y)$ and the Lefschetz number

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#calculus #real-analysis #ordinary-differential-equations #manifolds #differential-topology
128
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Definition of the tangent bundle in Guillemin and Pollack

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#differential-geometry #manifolds #differential-topology #smooth-manifolds #tangent-bundle
686
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Tangent space to the image of a vector field

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#real-analysis #differential-geometry #manifolds #differential-topology #smooth-manifolds
1.4k
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Tangent Space Coincides with Null Space of Jacobian When Full Rank

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#differential-geometry #optimization #manifolds #implicit-function-theorem
393
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Kernel of Cotangent Vector Equals Tangent Space to Submanifold

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#differential-geometry #manifolds #differential-forms
450
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The topology on coordinate charts of a manifold

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#real-analysis #general-topology #manifolds
98
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Submanifold proof

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#differential-geometry #manifolds
977
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Is $SO(n)$ a normal subgroup of $SO(n+1)$?

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#matrices #differential-geometry #manifolds #riemannian-geometry
405
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An affine bundle has a global section?

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#geometry #differential-geometry #manifolds #differential-topology #vector-bundles
135
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How to understand following vector fields on manifold

Published on
#manifolds #vector-fields
644
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Does partition of unity implies second countable?

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#real-analysis #manifolds #second-countable
374
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Derivations as abstract vector space

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#differential-geometry #manifolds #topological-vector-spaces

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