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Tangent vectors on the boundary of a manifold.

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#differential-geometry #manifolds #smooth-manifolds #tangent-spaces
362
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Quaternion Exponential map

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#lie-algebras #quaternions #tangent-spaces
125
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Tangent vectors at boundary points

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#smooth-manifolds #curves #manifolds-with-boundary #tangent-bundle #tangent-spaces
2.9k
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Coordinate basis of tangent space

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#differential-geometry #manifolds #tangent-spaces
43
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Domain of the derivative

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#multivariable-calculus #derivatives #differential-geometry #tangent-spaces
63
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Rigiorous justification for method of characteristics applied to quasilinear PDEs

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#ordinary-differential-equations #partial-differential-equations #tangent-spaces
41
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If $u$ is an extremal point of a functional $E$ and $γ$ is a smooth curve with $γ(0)=u$, then $0$ is an extremal point of $E\circ\gamma$

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#functional-analysis #differential-geometry #tangent-spaces #extreme-value-theorem
600
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Definition of Left Invariant Vector Fields

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#differential-geometry #lie-groups #lie-algebras #symplectic-geometry #tangent-spaces
2.8k
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What does the adjoint action of a Lie group on its Lie algebra, ${\rm Ad}:G\times{\frak g\to g}$, actually give us?

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#differential-geometry #lie-groups #lie-algebras #symplectic-geometry #tangent-spaces
1.3k
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Coadjoint action of Lie group on dual of its Lie algebra

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#differential-geometry #lie-groups #lie-algebras #symplectic-geometry #tangent-spaces
4k
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Why are the partial derivatives a basis of the tangent space?

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#differential-forms #tangent-spaces
137
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Construction of the Tangent Bundle

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#algebraic-geometry #reference-request #tangent-spaces
935
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Motivation for defining a tangent vector as an equivalence class of curves

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#manifolds #tangent-spaces
167
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If a real function has a zero of order $n$, then except for a diffeomorphism, it is $x^n$.

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#calculus #differential-geometry #taylor-expansion #differential-topology #tangent-spaces
1.1k
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Tangent Space for Torus

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#manifolds #smooth-manifolds #tangent-bundle #tangent-spaces

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