Affiliation:
1. Louisiana Tech University Ruston America
Abstract
Abstract
On a 7-manifold with a G
2-structure, we study conformal symmetries — which are vector fields whose flow generate conformal transformations of the G
2-structure. In particular, we focus on compact 7-manifolds and the condition that the Lee form of the G
2-structure is closed. Among other observations, we show that conformal symmetries are determined within a conformal class of the G
2-structure by the symmetries of a unique (up to homothety) G
2-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.