ON THE COTANGENT BUNDLE AND UNIT COTANGENT BUNDLE WITH A GENERALIZED CHEEGER-GROMOLL METRIC

Zagane A., Djaa N. E., GEZER A.

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, cilt.38, sa.1, ss.153-178, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.22190/fumi221101011z
  • Dergi Adı: FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.153-178
  • Anahtar Kelimeler: Horizontal lift and vertical lift, cotangent bundles, generalized Cheeger-Gromoll metric, curvature tensor
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, we consider a generalized Cheeger-Gromoll metric on a cotangent bundle over a Riemannian manifold, which is obtained by rescaling the vertical part of the Cheeger-Gromoll metric by a positive differentiable function. Firstly, we investigate the curvature properties on the cotangent bundle with the generalized CheegerGromoll metric. Secondly, we introduce the unit cotangent bundle equipped with this metric, where we present the formulas of the Levi-Civita connection and also all formulas of the Riemannian curvature tensors of this metric. Finally, we study the geodesics on the unit cotangent bundle with respect to this metric.