Spinorial Characterization of CR Structures, I

TL;DR

This paper characterizes specific CR structures on Riemannian Spin$^c$ manifolds using partially pure spinor fields and explores the geometry of such manifolds satisfying generalized Killing equations.

Contribution

It introduces a spinorial characterization of certain CR structures of arbitrary codimension on Riemannian Spin$^c$ manifolds and studies associated geometric properties.

Findings

CR structures characterized by partially pure spinors

Existence of generalized Killing spinors on these manifolds

New insights into the geometry of Spin$^c$ manifolds with special spinors

Abstract

We characterize certain CR structures of arbitrary codimension (different from 3, 4 and 5) on Riemannian Spin$^c$ manifolds by the existence of a Spin$^c$ structure carrying a strictly partially pure spinor field. Furthermore, we study the geometry of Riemannian Spin$^c$ manifolds carrying a strictly partially pure spinor which satisfies the generalized Killing equation in prescribed directions.