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Keywords:
harmonic unit vector field; minimal unit vector field; Lie group; Riemannian symmetric space; isometric action
harmonic unit vector field; minimal unit vector field; Lie group; Riemannian symmetric space; isometric action
Summary:
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.
References:
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