Biharmonic maps into Sol and Nil spaces

Y. -L. Ou; Z. -P. Wang

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arXiv · math/0612329

Biharmonic maps into Sol and Nil spaces

Y. -L. Ou·Z. -P. Wang

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Abstract

In this paper, we study biharmonic maps into Sol and Nil spaces, two model spaces of Thurston's 3-dimensional geometries. We characterize non-geodesic biharmonic curves in Sol space and prove that there exists no non-geodesic biharmonic helix in Sol space. We also show that a linear map from a Euclidean space into Sol or Nil space is biharmonic if and only if it is a harmonic map, and give a complete classification of such maps.

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BibTeX RIS

Y. -L. Ou, Z. -P. Wang. 2006-12-13. Biharmonic maps into Sol and Nil spaces. https://arxiv.org/abs/math/0612329

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