11 papers
Torsion parallel pure spinors on neutral manifolds
Alejandro Gil-GarcÃa
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…
Sasakian manifolds and spin-c Killing spinors
Alejandro Gil-GarcÃa, C. S. Shahbazi
Using the theory of complex spinorial forms, we prove that an odd-dimensional Riemannian manifold admits a pure spin-c Killing spinor with a real Killing constant $α\in\mathbb{R}^…
Almost abelian pseudo-Kähler Lie algebras
Diego Conti, Alejandro Gil-GarcÃa
We study invariant pseudo-Kähler structures on a solvmanifold such that the Lie algebra is almost abelian, that is ,…
Complex spinorial forms, Brinkmann four-manifolds, and self-dual bundle gerbes
Alejandro Gil-GarcÃa, C. S. Shahbazi
We develop the differential theory of complex spinorial forms associated with irreducible complex spinors across all dimensions and signatures. This framework enables the study of…
Left-invariant harmonic spinors on three-dimensional Lie groups
Alejandro Gil-GarcÃa, Giovanni Russo
We study the existence of left-invariant harmonic spinors on three-dimensional Lie groups equipped with a left-invariant pseudo-Riemannian metric. An existing formula for the spin…
The algebraic square of an irreducible complex spinor
Alejandro Gil-GarcÃa, C. S. Shahbazi
We characterize, in every dimension and signature, the algebraic squares of an irreducible complex spinor as a pair of exterior forms satisfying a prescribed system of algebraic re…