Schouten and Vr˘anceanu Connections on Golden Manifolds

Abstract

In this paper, we study two special linear connections, which are called Schouten and Vr˘anceanuconnections, defined by an arbitrary fixed linear connection on a differentiable manifoldadmitting a golden structure. The golden structure defines two naturally complementary projectionoperators splitting the tangent bundle into two complementary parts, so there are two globallycomplementary distributions of the tangent bundle. We examine the conditions of parallelismfor both of the distributions with respect to the fixed linear connection under the assumptionthat it is either the Levi-Civita connection or is not. We investigate the concepts of halfparallelism and anti half parallelism for each of the distributions with respect to the Schoutenand Vr˘anceanu connections. We research integrability conditions of the golden structure and itsassociated distributions from the viewpoint of the Schouten and Vr˘anceanu connections. Finally,we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vr˘anceanuconnections.