| 21. | For example, every solenoidal vector field can be written as
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| 22. | The diffeomorphism group are flows with vector fields absolutely integrable in Sobolev norm
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| 23. | Thus this vector field has a magnitude of 2 in units of ?.
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| 24. | A vector field is an assignment of a tangent vector to each point.
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| 25. | Now, define a vector field \ mathbf { v } on U by
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| 26. | From this theorem one deduces the Poincar?Hopf theorem for vector fields.
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| 27. | Denotes the Schouten & ndash; Nijenhuis bracket on multi-vector fields.
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| 28. | Thus solenoidal vector fields are precisely those that have volume-preserving flows.
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| 29. | In our expression for the metric, note that are null vector fields.
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| 30. | Therefore, is a timelike vector field, while are spacelike vector fields.
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