Invariant Minimal Unit Vector Fields on Lie Groups

Springer Science and Business Media LLC - Tập 40 - Trang 123-133 - 2000
K. Tsukada1, L. Vanhecke2
1Department of Mathematics, Ochanomizu University, Tokyo, Japan
2Department of Mathematics, Katholieke Universiteit Leuven, Leuven, Belgium

Tóm tắt

We provide a new characterization of invariant minimal unit vector fields on Lie groups and use it to construct some new examples. In particular, we determine all these vector fields on three-dimensional Lie groups.

Tài liệu tham khảo

J. Berndt, F. Tricerri and L. Vanhecke, Generalized Heisenberg groups and Damek-Ricci harmonic spaces, Lecture Notes in Math. 1598, Springer-Verlag, Berlin, Heidelberg, New York, 1995. E. Boeckx and L. Vanhecke, Harmonic and minimal radial vector fields, Acta Math. Hungar., to appear. E. Boeckx and L. Vanhecke, Harmonic and minimal vector fields on tangent and unit tangent bundles, Differential Geom. and its Appl., to appear. O. Gil-Medrano and E. Llinares-Fuster, Minimal unit vector fields, preprint, 1998. H. Gluck and W. Ziller, On the volume of a unit vector field on the three-sphere, Comment. Math. Helv. 61 (1986), 177–192. J. C. GonzÁlez-DÁvila and L. Vanhecke, Examples of minimal unit vector fields, Ann. Global Anal. Geom., to appear. J. C. GonzÁlez-DÁvila and L. Vanhecke, Minimal and harmonic characteristic vector fields on three-dimensional contact metric manifolds, preprint, 1999. J. Milnor, Curvature of left invariant metrics on Lie groups, Adv. in Math. 21 (1976), 293–329. T. H. Wolter, Einstein metrics on solvable groups, Math. Z. 206 (1991), 457–471.