Schouten and Vranceanu Connections on Golden Manifolds


Gok M., KELEŞ S. , KILIÇ E.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.12, ss.169-181, 2019 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 12 Konu: 2
  • Basım Tarihi: 2019
  • Dergi Adı: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Sayfa Sayıları: ss.169-181

Özet

In this paper, we study two special linear connections, which are called Schouten and Vranceanu 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 Vranceanu connections. We research integrability conditions of the golden structure and its associated distributions from the viewpoint of the Schouten and Vranceanu connections. Finally, we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vranceanu connections.