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How to understand following vector fields on manifold

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#manifolds #vector-fields
689
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Lift of vector field in smooth manifold

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#differential-geometry #riemannian-geometry #smooth-manifolds #vector-fields
444
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kernel of $1$-form defines a distribution

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#differential-geometry #determinant #differential-forms #vector-fields
530
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How can I check whether the given function or vector field is path-dependent or path-independent?

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#vector-analysis #vector-fields #line-integrals
70
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How to prove expressions using field properties?

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#linear-algebra #vector-fields
2.3k
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What does Gradient actually mean?

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#vectors #derivatives #vector-fields
956
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work done by a vector field from a potential function

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#vector-fields #line-integrals
124
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$X\in\mathfrak{X}(M)$ and $df(X)$ is bounded $\Rightarrow X$ complete

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#differential-geometry #smooth-manifolds #vector-fields
1.1k
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Vector fields commute implies flows can be written as composition of individual flows

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#differential-geometry #manifolds #smooth-manifolds #vector-fields
240
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Proving function space is a vector space

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#linear-algebra #field-theory #vector-fields
48
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Which of these two definitions is wrong?

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#vector-analysis #vector-fields
153
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Translating a vector field along the x-axis?

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#linear-algebra #vectors #vector-fields
2.3k
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Determine stability of the origin in a system with two zero eigenvalues

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#ordinary-differential-equations #dynamical-systems #vector-fields #stability-in-odes #stability-theory
333
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Lifts of flows to the universal cover

Published on
#differential-geometry #differential-topology #dynamical-systems #geometric-topology #vector-fields
531
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Conservative field and curl

Published on
#multivariable-calculus #vector-fields

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