Let (M = G/H; g) denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.

Harmonicity of vector fields on four-dimensional generalized symmetric spaces

CALVARUSO, Giovanni
2012-01-01

Abstract

Let (M = G/H; g) denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/362169
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