Geodesic
Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces $G_2$ and $G_2/SO(4)$
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 1, pp. 101-109.

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The exceptional compact symmetric spaces $G_2$ and $G_2/SO(4)$ admit cohomogeneity one isometric actions with two totally geodesic singular orbits. These singular orbits are not reflective submanifolds of the ambient spaces. We prove that the radial unit vector fields associated to these isometric actions are harmonic and minimal.
Classification : 53C35, 53C40, 53C42, 53C43, 57S15
Keywords: harmonic unit vector field; minimal unit vector field; Lie group; Riemannian symmetric space; isometric action 
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Verhóczki, László. Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces $G_2$ and $G_2/SO(4)$. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 1, pp. 101-109. http://geodesic.mathdoc.fr/item/AUPO_2012__51_1_a7/