Biharmonic maps into Sol and Nil spaces
Differential Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0612329,
title = {Biharmonic maps into Sol and Nil spaces},
author = {Y. -L. Ou and Z. -P. Wang},
journal= {arXiv preprint arXiv:math/0612329},
year = {2007}
}
Comments
18pages