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

  • 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: complete lift, Harmonic maps, Riemannian extension, Sasaki lift
  • Gazi University Affiliated: Yes

Abstract

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.