Some Problems Concerning with Sasaki Metric on the Second-Order Tangent Bundles

Magden A., GEZER A., Karaca K.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.13, sa.2, ss.75-86, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.36890/iejg.750905
  • Dergi Adı: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.75-86
  • Anahtar Kelimeler: Curvature tensor field, lifts, second-order tangent bundle, statistical structure, weakly symmetry, SYMMETRY
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, we consider a second-order tangent bundle equipped with Sasaki metric over a Riemannian manifold. All forms of curvature tensor fields are computed. We obtained the relation between the scalar curvature of the base manifold and the scalar curvature of the second-order tangent bundle and presented some geometric results concerning with kinds of curvature tensor fields. Also, we search the weakly symmetry property of the second-order tangent bundle. Finally, we end our paper with statistical structures on the second-order tangent bundle.