Spinors on Kahler-Norden manifolds

Abstract

It is known that the complex spin group Spin(n,C) is the universal covering group of complex orthogonal group SO(n,C). In this work we construct a new kind of spinors on some classes of Kahler-Norden manifolds. The structure group of such a Kahler-Norden manifold is SO(n,C) and has a lifting to Spin(n,C). We prove that the Levi-Civita connection on M is an SO(n,C)-connection. By using the spinor representation of the group Spin(n,C), we define the spinor bundle S on M. Then we define covariant derivative operator ? on S and study some properties of ?. Lastly we define Dirac operator on S