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

2016/01/28 by Lokman Bilen, Bilen, Lokman, Aydin Gezer +1
Mathematics · #53A45 #53C07 #53C35 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A45 #msc:53C07 #msc:53C35

paper · pdf · doi:10.48550/arxiv.1601.07696

arxiv created 2016/01/28 · arxiv updated 2016/01/29

Abstract

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

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