Let M be an n−dimensional differentiable manifold with a symmetric connection ∇ and T * M be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension g ∇,c on T * M defined by means of a symmetric (0, 2)-tensor field c on M. We get the conditions under which T * M endowed with the horizontal lift H J of an almost complex structure J and with the metric g ∇,c is a Kähler-Norden manifold. Also curvature properties of the Levi-Civita connection and another metric connection of the metric g ∇,c are presented.2000 Mathematics Subject Classification. Primary 53C07, 53C55; Secondary 53C22.
In this paper, we consider a pseudo-Riemannian manifold equipped with a Kähler–Norden–Codazzi golden structure. For such a manifold, we study curvature properties. Also, we define special connections of the first type and of the second type on the manifold, which preserve the associated twin Norden golden metric and satisfy some special conditions and present some results concerning them.
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 ∇ 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 ∇. Secondly, we study conditions for (T * M, g ∇,c ) to be semi-symmetric, Ricci semi-symmetric, Z semi-symmetric or locally conharmonically flat with respect to the metric connection ∇. Finally, we present some results concerning the Schouten-Van Kampen connection associated to the Levi-Civita connection ∇ of the modified Riemannian extension g ∇,c .Mathematics subject classification 2010. 53C07, 53C35, 53A45.
The present paper deals with the classification of infinitesimal fibre-preserving conformal transformations on the tangent bundle, equipped with the Cheeger-Gromoll metric
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