Spinors and Dirac operator on Kahler Norden manifolds

In this thesis, the constructibility of a spinor theory which is similar to theclasical theory of spinors is investigated on a 2n dimensional manifold withstructure group SO(n;C). Firstly, it is pointed out a relationship between thegroups SO(n;C) and Spin(n;C); then the spinor representation of the groupSpin(n;C) is defined. It is observed that the Kahler-Norden and the complexRiemannian manifolds have structure group O(n;C). The explicit expressionsof some diferential operators on Kahler-Norden manifolds are given. A certainclasses of Kahler-Norden manifolds are defined as Kahler-Norden spin mani-folds. By using the spinor representation of the group Spin(n;C), the spinorbundle S is constructed on a Kahler-Norden spin manifold. For a spinor ¯fieldon M some alternative expressions are given. It is proved that the Levi-Civitaconnection on M is an SO(n;C) connection, then by using this fact a covari-ant derivative operator on S is defined. The Clifford product of a vector fieldwith a spinor field is defined. On the spinor bundle S the Dirac operator Dis defined. Lastly, it is proved that the Dirac operator D satisfies a formulawhich is similar to the Schrödinger-Lichnerowicz formula in the classical cases.