Journal of Geometry

, 109:6 | Cite as

On metric connections with torsion on the cotangent bundle with modified Riemannian extension

  • Lokman Bilen
  • Aydin Gezer


Let M be an n-dimensional differentiable manifold equipped with a torsion-free linear connection \(\nabla \) and \(T^{*}M\) its cotangent bundle. The present paper aims to study a metric connection \(\widetilde{ \nabla }\) with nonvanishing torsion on \(T^{*}M\) with modified Riemannian extension \({}\overline{g}_{\nabla ,c}\). First, we give a characterization of fibre-preserving projective vector fields on \((T^{*}M,{}\overline{g} _{\nabla ,c})\) with respect to the metric connection \(\widetilde{\nabla }\). Secondly, we study conditions for \((T^{*}M,{}\overline{g}_{\nabla ,c})\) to be semi-symmetric, Ricci semi-symmetric, \(\widetilde{Z}\) semi-symmetric or locally conharmonically flat with respect to the metric connection \( \widetilde{\nabla }\). Finally, we present some results concerning the Schouten–Van Kampen connection associated to the Levi-Civita connection \( \overline{\nabla }\) of the modified Riemannian extension \(\overline{g} _{\nabla ,c}\).


Cotangent bundle fibre-preserving projective vector field metric connection Riemannian extension semi-symmetry 

Mathematics Subject Classification

53C07 53C35 53A45 


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Copyright information

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Authors and Affiliations

  1. 1.Department of Mathematics and Computer, Faculty of Science and LettersIgdir UniversityIgdirTurkey
  2. 2.Department of Mathematics, Faculty of ScienceAtaturk UniversityErzurumTurkey

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