Work

On the existence of critical compatible metrics on contact 3‐manifolds

Year: 2024

Type: article

Abstract: We disprove the generalized Chern–Hamilton conjecture on the existence of critical compatible metrics on contact 3‐manifolds. More precisely, we show that a contact 3‐manifold admits a critical compatible metric for the Chern–Hamilton energy functional if and only if it is Sasakian or its associated Reeb flow is ‐conjugate to an algebraic Anosov flow modeled on . In particular, this yields a complete topological classification of compact 3‐manifolds that admit critical compatible metrics. As a corollary, we prove that no contact structure on admits a critical compatible metric and that critical compatible metrics can only occur when the contact structure is tight.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.13183

Authors: Y. Mitsumatsu, D. Peralta‐Salas, R. Slobodeanu

Institutions: Chuo University, Consejo Superior de Investigaciones Científicas, Institute of Mathematical Sciences, University of Bucharest

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funders: Fundación BBVA, Banco Bilbao Vizcaya Argentaria, Japan Society for the Promotion of Science, Agencia Estatal de Investigación