Journal of Geometry

, 109:6 | Cite as

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

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Abstract

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 \(\overline{g} _{\nabla ,c}\).

Keywords

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

© Springer International Publishing AG, part of Springer Nature 2018

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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