Complex Generalized Killing Spinors on Riemannian Spin c Manifolds

Abstract

In this paper, we extend the study of generalized Killing spinors on Riemannian Spinc manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are always real spinc Killing spinors or imaginary generalized Spinc Killing spinors, providing that the dimension of the manifold is greater or equal to 4. Moreover, we examine which Riemannian Spinc manifolds admit imaginary and imaginary generalized Killing spinors.