Cross sections to flows via intrinsically harmonic forms

Slobodan N. Simić

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arXiv · 1906.02705

Cross sections to flows via intrinsically harmonic forms

Slobodan N. Simić

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Abstract

We establish a new criterion for the existence of a global cross section to a non-singular volume-preserving flow on a compact manifold. Namely, if $Φ$ is a non-singular smooth flow on a compact, connected manifold $M$ with a smooth invariant volume form $Ω$, then $Φ$ admits a global cross section if and only if the $(n-1)$-form $i_X Ω$ is intrinsically harmonic, that is, harmonic with respect to some Riemannian metric on $M$.

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Slobodan N. Simić. 2019-06-06. Cross sections to flows via intrinsically harmonic forms. https://arxiv.org/abs/1906.02705

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