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A study on complex semi-symmetric non-metric F-connections on anti-Kähler manifolds

  • Cagri Karaman
  • Aydin Gezer
Article

Abstract

In this paper, we have considered an anti-Kähler manifold (MgF) admitting a complex semi-symmetric non-metric F-connection \({\widetilde{\nabla }}\). First we study the properties of the curvature tensor, the conharmonic curvature tensor and the conformal curvature tensor of the connection \({\widetilde{\nabla }}\). Also, we investigate the condition for the anti-Kähler manifold (MgF) to be Einstein space with respect to the connection \({\widetilde{\nabla }}\). Finally, we define the dual connection of the connection \({\widetilde{\nabla }}\) and present some results related to its curvature tensors.

Keywords

Complex structure Curvature tensor Semi-symmetric non-metric F-connection Tachibana operator Dual connection 

Mathematics Subject Classification

53B20 53B15 53B35 

Notes

Acknowledgements

We would like to thank the reviewer for his\(\backslash \)her thoughtful comments and efforts towards improving our manuscript.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Oltu Faculty of Earth Science, Geomatics EngineerAtaturk UniversityErzurumTurkey
  2. 2.Faculty of Science, Department of MathematicsAtaturk UniversityErzurumTurkey

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