Spin^t structure and dirac operator on riemannian manifolds

In this thesis, the constructability of Spin^T spinor theory similar to known Spin^c spinor theory is investigated on the orientable Riemannian manifolds. Firstly, the group Spin^T(n) is defined and some properties of this group are studied. In low dimensions, the group Spin^T(n) is examined. With the aid of the representation of the group Spin^c(n) the representation of the group Spin^T(n) is given. The Spin^T- structure is defined on the orientable Riemannian manifolds. By using the representation of the group Spin^T(n), the Spin^T spinor bundle is constructed. Then, by the way of the Levi-Civita connection on the orientable Riemannian manifolds, the covariant derivative operator is defined on Spin^T spinor bundle. By using this covariant derivative, Spin^T Dirac operator is defined and some properties of Spin^T Dirac operator is investigated. Lastly, Spin^T Dirac operator is showned to provide a formula similar to the Schrödinger-Lichnerowicz type formula.