2016/10/14 by Rafael Herrera, Herrera, Rafael, Roger Nakad +3
Mathematics · #32V05 #53C10 #53C25 #53C27 #58J50 #58J60 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1610.04497
openalex publication_date 2016/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Spinc, r 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 Spinc spinors.