Spinorially twisted Spin structures, III: CR structures
Differential Geometry
2016-10-17 v1
Abstract
We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin structure carrying a partially pure spinor field. We study various integrability conditions of the almost CR structure in our spinorial setup, including the classical integrability of a CR structure as well as those implied by Killing-type conditions on the partially pure spinor field. In the codimension one case, we develop a spinorial description of strictly pseudoconvex CR manifolds, metric contact manifolds and Sasakian manifolds. Finally, we study hypersurfaces of Kaehler manifolds via partially pure Spin spinors.
Cite
@article{arxiv.1610.04497,
title = {Spinorially twisted Spin structures, III: CR structures},
author = {Rafael Herrera and Roger Nakad and Ivan Tellez},
journal= {arXiv preprint arXiv:1610.04497},
year = {2016}
}