Journal of Nonlinear Mathematical Physics

Volume 17, Issue 1, March 2013, Pages 27 - 34

Spinors on Kahler–Norden Manifolds

Authors
Nedim Değirmenci*, Şenay Karapazar
Department of Mathematics, University of Anadolu, Eskisehir, 26470, Turkey
Corresponding Author
Nedim Değirmenci
Received 15 January 2009, Accepted 6 August 2009, Available Online 7 January 2021.
DOI
https://doi.org/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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
17 - 1
Pages
27 - 34
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925110000568How to use a DOI?
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
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  - https://doi.org/10.1142/S1402925110000568
ID  - Değirmenci2021
ER  -