Work

Conformal structures with $$G_2$$-symmetric twistor distribution

Year: 2025

Type: article

Abstract: For any 4D split-signature conformal structure, there is an induced twistor distribution on the 5D space of all self-dual totally null 2-planes, which is (2, 3, 5) when the conformal structure is not anti-self-dual. Several examples where the twistor distribution achieves maximal symmetry (the split-real form of the exceptional simple Lie algebra of type $$\textrm{G}_2$$ G 2 ) were previously known, and these include fascinating examples arising from the rolling of surfaces without twisting or slipping. We establish a complete local classification result for achieving maximal symmetry of the twistor distribution, identified among those homogeneous 4D split-conformal structures for which the conformal symmetry algebra induces a multiply-transitive action on the 5D space. Furthermore, we discuss geometric properties of these conformal structures such as their curvature, holonomy, and existence of Einstein representatives.

Source: Analysis and Mathematical Physics

DOI: 10.1007/s13324-025-01039-9

Authors: Pawel Nurowski, Katja Sagerschnig, Dennis The

Institutions: Center for Theoretical Physics, Guangdong Technion-Israel Institute of Technology, Polish Academy of Sciences, UiT The Arctic University of Norway

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Universitetet i Tromsø