Schouten and Vranceanu Connections on Golden Manifolds
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Tarih
2019
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International Electronic Journal of Geometry
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info:eu-repo/semantics/openAccess
Özet
Öz:In this paper, we study two special linear connections, which are called Schouten and Vr˘anceanu 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 distributions 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 Vr˘anceanu connections. We research integrability conditions of the golden structure and its associated 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˘anceanu connections.
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International Electronic Journal of Geometry
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Künye
GÖK M,KELEŞ S,KILIÇ E (2019). Schouten and Vr˘anceanu Connections on Golden Manifolds. International Electronic Journal of Geometry, 12(2), 169 - 181.
