ON THE BIHARMONICITY OF VECTOR FIELDS ON PSEUDO-RIEMANNIAN MANIFOLDS

Alem A., Kacimi B., ÖZKAN M.

HONAM MATHEMATICAL JOURNAL, sa.2, ss.300-315, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2023
  • Doi Numarası: 10.5831/hmj.2023.45.2.300
  • Dergi Adı: HONAM MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.300-315
  • Gazi Üniversitesi Adresli: Evet

Özet

In this article, we deal with the biharmonicity of a vector field X viewed as a map from a pseudo-Riemannian manifold (M, g) into its tangent bundle TM endowed with the Sasaki metric gS. Precisely, we characterize those vector fields which are biharmonic maps, and find the relationship between them and biharmonic vector fields. Afterwards, we study the biharmonicity of left-invariant vector fields on the three dimen-sional Heisenberg group endowed with a left-invariant Lorentzian metric. Finally, we give examples of vector fields which are proper biharmonic maps on the Godel universe.