Schouten and Vrănceanu Connections on Golden Manifolds

Mustafa GÖK, Sadık KELEŞ, Erol KILIÇ
2019 International Electronic Journal of Geometry  
In this paper, we study two special linear connections, which are called Schouten and Vrȃnceanu connections, defined by an arbitrary fixed linear connection on a differentiable manifold admitting a golden structure. The golden structure defines two naturally complementary projection operators splitting the tangent bundle into two complementary parts, so there are two globally complementary distributions of the tangent bundle. We examine the conditions of parallelism for both of the
more » ... with respect to the fixed linear connection under the assumption that it is either the Levi-Civita connection or is not. We investigate the concepts of half parallelism and anti half parallelism for each of the distributions with respect to the Schouten and Vrȃnceanu connections. We research integrability conditions of the golden structure and its associated distributions from the viewpoint of the Schouten and Vrȃnceanu connections. Finally, we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vrȃnceanu connections.
doi:10.36890/iejg.628070 fatcat:xnzfq7ito5eh5jani4rmgjxo3y