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Consider symplectic vector fields $X,Y$ and a symplectic connection $\nabla$. Is $\nabla_{X}Y$ symplectic?

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#differential-geometry #vector-fields #symplectic-geometry #connections #lie-derivative
334
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Calculate covariant divergence

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#general-relativity #vector-fields
352
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Smooth extension of a coordinate vector field

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#smooth-manifolds #vector-fields
242
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Euler field is invariant under the cotangent lift

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#differential-geometry #vector-fields #symplectic-geometry
663
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Vector fields on projective space

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#algebraic-geometry #vector-fields
271
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Are the gradients of three dimensional surfaces maximised about their perpendicular direction?

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#vectors #derivatives #vector-fields
557
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Physical interpretation of divergence for a velocity vector field

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#vector-fields #divergence-operator
117
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About the definition of divergence and curl

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#multivariable-calculus #vector-fields #divergence-operator #curl
406
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(Negative) Gradient and Orientability of its flow.

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#differential-geometry #vector-fields #orientation #morse-theory #gradient-flows
26
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Can we get short formula to get the curl of a function $ M \hat{i} + N \hat{j} +O \hat{k} $

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#vector-fields
406
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What is the meaning of $A. \nabla $?

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#vector-analysis #vector-fields
325
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Monotonicity of vector fields

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#functional-analysis #functions #vectors #vector-fields #monotone-functions
1k
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How can a vector field eat a smooth function?

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#differential-geometry #vector-fields
546
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Cotangent lift of the commutator of 2 vector fields

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#vector-fields #symplectic-geometry #co-tangent-space
58
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How do I simplify vector multiplied by nabla?

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#vectors #derivatives #vector-fields

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