Honam Mathematical Journal (호남수학학술지)

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ON THE BIHARMONICITY OF VECTOR FIELDS ON PSEUDO-RIEMANNIAN MANIFOLDS

  • Amina Alem (Department of Mathematics, Faculty of Exact Sciences, University of Mascara) ;
  • Bouazza Kacimi (Department of Mathematics, Faculty of Exact Sciences, University of Mascara) ;
  • Mustafa Ozkan (Department of Mathematics, Faculty of Sciences, Gazi University)
  • Received : 2022.11.05
  • Accepted : 2023.01.16
  • Published : 2023.06.01
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Abstract

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 dimensional Heisenberg group endowed with a left-invariant Lorentzian metric. Finally, we give examples of vector fields which are proper biharmonic maps on the Gödel universe.

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References

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