Geodesic
Invariant harmonic unit vector fields on Lie groups
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 2, pp. 377-403 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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We provide a new characterization of invariant harmonic unit vector fields on Lie groups endowed with a left-invariant metric. We use it to derive existence results and to construct new examples on Lie groups equipped with a bi-invariant metric, on three-dimensional Lie groups, on generalized Heisenberg groups, on Damek-Ricci spaces and on particular semi-direct products. In several cases a complete list of such vector fields is given. Furthermore, for a lot of the examples we determine associated harmonic maps from the considered group into its unit tangent bundle equipped with the associated Sasaki metric. 
@article{BUMI_2002_8_5B_2_a6,
     author = {Gonz\'alez-D\'avila, J. C. and Vanhecke, L.},
     title = {Invariant harmonic unit vector fields on {Lie} groups},
     journal = {Bollettino della Unione matematica italiana},
     pages = {377--403},
     year = {2002},
     volume = {Ser. 8, 5B},
     number = {2},
     zbl = {1097.53033},
     mrnumber = {MR1911197},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_2_a6/}
}
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González-Dávila, J. C.; Vanhecke, L. Invariant harmonic unit vector fields on Lie groups. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 2, pp. 377-403. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_2_a6/