Spinorially Twisted Spin Structures. II: Twisted Pure Spinors, Special Riemannian Holonomy and Clifford Monopoles

Abstract

We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special Kähler holonomy. Motivated by certain curvature identities satisfied by manifolds admitting parallel twisted pure spinors, we also introduce the Clifford monopole equations as a natural geometric generalization of the Seiberg-Witten equations. We show that they restrict to the Seiberg-Witten equations in 4 dimensions, and that they admit non-trivial solutions on manifolds with special Riemannian holonomy.

References in corpus (9)

• Real pinor bundles and real Lipschitz structures
• Centralizers of spin subalgebras
• Almost even-Clifford hermitian manifolds with large automorphism group
• Clifford systems in octonionic geometry
• A note on the geometry and topology of almost even-Clifford Hermitian manifolds
• Spinorially twisted Spin structures, I: curvature identities and eigenvalue estimates
• Rigidity and Vanishing Theorems for Almost Even-Clifford Hermitian Manifolds
• Local Geometry of Even Clifford Structures on Conformal Manifolds
• Spin(9) and almost complex structures on 16-dimensional manifolds

Cited by in corpus (1)

• Spinorially twisted Spin structures, I: curvature identities and eigenvalue estimates