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Volume–preserving fieldX on a 3–manifold is the one that satisfies LXΩ ≡ 0 for some volume Ω. The Reeb vector field of a contact form is of volume–preserving, but not conversely. On the basis of Geiges–Gonzalo’s parallelization results, we obtain a volume–preserving sphere, which is a triple of everywhere linearly independent vector fields such that all their linear combinations with constant...
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