Cross-sections to flows and intrinsically harmonic forms
We establish a new criterion for the existence of a global cross-section to non-singular volume-preserving flows on compact manifolds. Namely, we show that 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 (Formula presented.) -form (Formula presented.) is intrinsically harmonic, that is, harmonic with respect to some Riemannian metric on M.
cross-sections, Flows, intrinsically harmonic differential forms
Mathematics and Statistics
Slobodan N. Simić. "Cross-sections to flows and intrinsically harmonic forms" Dynamical Systems (2023): 314-319. https://doi.org/10.1080/14689367.2023.2178389