Geometry of the Second-Order Tangent Bundles of Riemannian Manifolds

GEZER A., MAĞDEN A.

CHINESE ANNALS OF MATHEMATICS SERIES B, cilt.38, sa.4, ss.985-998, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s11401-017-1107-4
  • Dergi Adı: CHINESE ANNALS OF MATHEMATICS SERIES B
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.985-998
  • Anahtar Kelimeler: Almost product structure, Killing vector field, Metric connection, Riemannian metric, Second-order tangent bundle
  • Atatürk Üniversitesi Adresli: Evet

Özet

Let (M, g) be an n-dimensional Riemannian manifold and (TM)-M-2 be its second order tangent bundle equipped with a lift metric (g) over tilde. In this paper, first, the authors construct some Riemannian almost product structures on ((TM)-M-2, (g) over tilde) and present some results concerning these structures. Then, they investigate the curvature properties of ((TM)-M-2, (g) over tilde Finally, they study the properties of two metric connections with nonvanishing torsion on ((TM)-M-2, (g) over tilde): The H-lift of the Levi-Civita connection of g to (TM)-M-2, and the product conjugate connection defined by the Levi-Civita connection of (g) over tilde and an almost product structure.