Biharmonic Curves in Three-Dimensional Generalized Symmetric Spaces


  • Mansour Belarbi
  • Hichem Elhendi
  • Lakehal Belarbi



Generalized Symmetric Spaces, Left-Invariant Metrics, Harmonic Curves, Biharmonic Curves, Pseudo-Riemannian Metrics.


In this paper, we study biharmonic curves in three-dimensio -nal generalized symmetric spaces, equipped with a left-invariant pseudo- Riemannian metric. We characterize non-geodesic biharmonic curves in three-dimensional generalized symmetric spaces and prove that there ex- ists no non-geodesic biharmonic spacelike helix in three-dimensional gen- eralized symmetric spaces. We also show that a linear map from a Eu- clidean space in three-dimensional generalized symmetric spaces is bihar- monic if and only if it is a harmonic map, and give a complete classification of such maps.


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How to Cite

Belarbi, M., Elhendi, H., & Belarbi, L. (2022). Biharmonic Curves in Three-Dimensional Generalized Symmetric Spaces. The Journal of the Indian Mathematical Society, 89(3-4), 263–277.