Year: 2025
Type: article
Abstract: In this paper, we study transversely holomorphic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove that for Anosov flows on smooth compact manifolds, the strong unstable (respectively, stable) distribution is integrable to complex manifolds, on which the flow acts holomorphically. Furthermore, assuming its complex dimension to be one, it is uniquely integrable to complex affine one-dimensional manifolds, each moreover affinely diffeomorphic to [Formula: see text], on which the flow acts affinely. In this case, the weak stable (respectively, unstable) foliation is transversely holomorphic, and even transversely projective if the flow is assumed to be topologically transitive. By combining these facts in low dimensions, our main result is as follows : if a transversely holomorphic Anosov flow on a smooth compact five-dimensional manifold is topologically transitive, then it is either [Formula: see text] orbit equivalent to the suspension of a hyperbolic automorphism of a complex torus, or, up to finite covers, [Formula: see text]-orbit equivalent to the geodesic flow of a compact hyperbolic manifold.
Source: Journal of Topology and Analysis
Author: Mounib Abouanass
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417303118
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