Some observations on conformal symmetries of G2-structures
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Christopher Lin
Abstract
On a 7-manifold with a G2-structure, we study conformal symmetries — which are vector fields whose flow generate conformal transformations of the G2-structure. In particular, we focus on compact 7-manifolds and the condition that the Lee form of the G2-structure is closed. Among other observations, we show that conformal symmetries are determined within a conformal class of the G2-structure by the symmetries of a unique (up to homothety) G2-structure whose Lee form is harmonic. On a related note, we also demonstrate that symmetries are split along fibrations when the Lee vector field is itself a symmetry.
Acknowledgements
The author would like to thank the referee for many useful comments.
Communicated by: P. Eberlein
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Articles in the same Issue
- Frontmatter
- Inequalities for f*-vectors of lattice polytopes
- Lower bound on the translative covering density of octahedra
- Variations on the Weak Bounded Negativity Conjecture
- Poisson Structures on moduli spaces of Higgs bundles over stacky curves
- Generalized Shioda–Inose structures of order 3
- Deformation cones of Tesler polytopes
- Some observations on conformal symmetries of G2-structures
- Characterization of the sphere and of bodies of revolution by means of Larman points
- Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
- The feet of orthogonal Buekenhout–Metz unitals
Articles in the same Issue
- Frontmatter
- Inequalities for f*-vectors of lattice polytopes
- Lower bound on the translative covering density of octahedra
- Variations on the Weak Bounded Negativity Conjecture
- Poisson Structures on moduli spaces of Higgs bundles over stacky curves
- Generalized Shioda–Inose structures of order 3
- Deformation cones of Tesler polytopes
- Some observations on conformal symmetries of G2-structures
- Characterization of the sphere and of bodies of revolution by means of Larman points
- Fractional-linear integrals of geodesic flows on surfaces and Nakai’s geodesic 4-webs
- The feet of orthogonal Buekenhout–Metz unitals
