Some Results on Harmonic Metrics

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Kadi F. Z., Kacimi B., ÖZKAN M.

Mediterranean Journal of Mathematics, vol.20, no.3, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.1007/s00009-023-02320-6
  • Journal Name: Mediterranean Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Harmonic maps, Sasaki lift, complete lift, Riemannian extension
  • Gazi University Affiliated: Yes


In this paper, we prove that the harmonicity of a metric on a pseudo-Riemannian manifold is equivalent to the harmonicity of both its Sasaki (resp. complete) lift metric on the tangent bundle and its Sasaki lift metric (resp. the Riemannian extension of the Levi-Civita connection) on the cotangent bundle, meanwhile we deal with harmonic metrics on warped product spaces. Some applications are included.