Volume 17, Issue 1, March 2010, Pages 27 - 34
Spinors on Kahler–Norden Manifolds
Received 15 January 2009, Accepted 6 August 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000568How to use a DOI?
- Keywords
- Spinor; Norden metric; anti-Kahler; complex orthogonal group; spin structure; complex spin group
- 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.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Nedim Değirmenci AU - Şenay Karapazar PY - 2021 DA - 2021/01/07 TI - Spinors on Kahler–Norden Manifolds JO - Journal of Nonlinear Mathematical Physics SP - 27 EP - 34 VL - 17 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000568 DO - 10.1142/S1402925110000568 ID - Değirmenci2021 ER -