English

On transversely holomorphic partially hyperbolic flows

Dynamical Systems 2026-01-30 v1 Differential Geometry

Abstract

In this paper, we study transversely holomorphic partially hyperbolic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove in the seven-dimensional case that under the assumption that the subcenter distribution is integrable to a flow invariant compact foliation with trivial holonomy, then the flow projects, by a smooth fiber bundle map, to a transversely holomorphic Anosov flow on a smooth five-dimensional manifold which is, in case of topological transitivity, either CC^\infty orbit equivalent to the suspension of a hyperbolic automorphism of a complex torus, or, up to finite covers, CC^\infty-orbit equivalent to the geodesic flow of a compact hyperbolic manifold.

Keywords

Cite

@article{arxiv.2601.21431,
  title  = {On transversely holomorphic partially hyperbolic flows},
  author = {Mounib Abouanass},
  journal= {arXiv preprint arXiv:2601.21431},
  year   = {2026}
}

Comments

32 pages. arXiv admin note: text overlap with arXiv:2601.20584, arXiv:2505.06572

R2 v1 2026-07-01T09:25:17.238Z