Schouten and Vranceanu Connections on Golden Manifolds

Gök M., Keleş S., Kılıç E.

International Electronic Journal of Geometry, cilt.12, sa.2, ss.169-181, 2019 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 2
  • Basım Tarihi: 2019
  • Dergi Adı: International Electronic Journal of Geometry
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.169-181
  • Anahtar Kelimeler: golden structure, Schouten connection, Vranceanu connection, parallelism, half parallelism, anti half parallelism, integrability, geodesic
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

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.