Vertical rescaled Cheeger-Gromoll metric and harmonicity on the cotangent bundle

Zagane A., Gezer A.

ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL, cilt.15, sa.3, ss.11-29, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.32513/asetmj/19322008221
  • Dergi Adı: ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.11-29
  • Anahtar Kelimeler: cotangent bundles, horizontal lift and vertical lift, vertical rescaled Cheeger-Gromoll metric, harmonic maps
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, we introduce the harmonicity on the cotangent bundle equipped with vertical rescaled Cheeger-Gromoll metric which rescales the vertical part by a non-zero differentiable function f. We establish a necessary and sufficient condition under which a covector field is harmonic with respect to this metric. We also construct some examples of harmonic vector fields. Finally, we study the harmonicity of a map between a Riemannian manifold and a cotangent bundle of another Riemannian manifold and vice versa.