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

  • Cagri Karaman
  • Aydin Gezer


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.


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

Mathematics Subject Classification

53B20 53B15 53B35 



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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