Revista Matemática Complutense· 2026Q1
Torsion parallel pure spinors on neutral manifolds
- 0citations
- Q1SCImago
- 2026year
Short summary
Pure spinors on neutral signature manifolds with torsion are characterized by their squares being decomposable middle-degree forms satisfying a duality condition.
AI-generated from the title and abstract; the full text is not read.
Key points
- Pure spinors on neutral signature manifolds with torsion have squares that are decomposable middle-degree differential forms.
- These forms satisfy a natural duality condition.
- In signature (4,4), non-pure spinors correspond to $\textrm{Spin}_0(4,3)$-structures.
- Real pure spinors parallel with torsion are characterized by an equivalent differential system for their squares.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We study irreducible real pure spinors on pseudo-Riemannian manifolds of neutral signature using the theory of real spinorial forms. We prove that the square of such a spinor is a decomposable differential form of middle degree satisfying a natural duality condition. In signature (4, 4), we show that non-pure spinors correspond to $$\textrm{Spin}_0(4,3)$$ Spin 0 ( 4 , 3 ) -structures, yielding an intrinsic algebraic characterization of these structures. In addition, we characterize real pure spinors parallel with respect to metric connections with torsion in terms of an equivalent differential system for their squares. As an application, we study left-invariant supersymmetric solutions of the NS-NS supergravity system on certain four-dimensional Lie groups.
The authors' abstract, as published at the source. Revista Matemática Complutense, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Applied Mathematics
Applied MathematicsMathematics