Parallel spinors for G2* and isotropic structures
Organizers
Speaker
Time
Tuesday, April 1, 2025 2:45 PM - 4:30 PM
Venue
A3-4-301
Online
Zoom 815 762 8413
(BIMSA)
Abstract
We obtain a correspondence between irreducible real parallel spinors on pseudo-Riemannian manifolds (M,g) of signature (4,3) and solutions of an associated differential system for three-forms that satisfy a homogeneous algebraic equation of order two in the Kähler-Atiyah bundle of (M,g). Applying this general framework, we obtain an intrinsic algebraic characterization of G2*-structures as well as the first explicit description of isotropic irreducible spinors in signature (4,3) that are parallel under a general connection on the spinor bundle. This description is given in terms of a coherent system of mutually orthogonal and isotropic one forms and follows from the characterization of the stabilizer of an isotropic spinor as the stabilizer of a highly degenerate three-form that we construct explicitly. Using this result, we show that isotropic spinors parallel under a metric connection with torsion exist when the connection preserves the aforementioned coherent system. This allows us to construct a natural class of metrics of signature (4,3) on R7 that admit spinors parallel under a metric connection with torsion. This is a joint work with C. S. Shahbazi based on https://arxiv.org/abs/2409.08553.