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Biharmonic Curves in Three-Dimensional Generalized Symmetric Spaces
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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.
Informatics Publishing Limited
Title: Biharmonic Curves in Three-Dimensional Generalized Symmetric Spaces
Description:
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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