Complex Generalized Killing Spinors on Riemannian Spin${}^c$ manifolds

Abstract

In this paper, we extend the study of generalized Killing spinors on Riemannian Spin${}^c$ manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are always real Spin${}^c$ Killing spinors or imaginary generalized Spin${}^c$ Killing spinors, providing that the dimension of the manifold is greater or equal to 4. Moreover, we classify Riemannian Spin${}^c$ manifolds carrying imaginary and imaginary generalized Killing spinors.

15 pages

References in corpus (2)

• Generalized Cylinders in Semi-Riemannian and Spin Geometry
• The Spin${}^c$ Dirac Operator on Hypersurfaces and Applications