Harmonicity of vector fields on four-dimensional generalized symmetric spaces

Giovanni Calvaruso

Open Mathematics (2012)

  • Volume: 10, Issue: 2, page 411-425
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Giovanni Calvaruso. "Harmonicity of vector fields on four-dimensional generalized symmetric spaces." Open Mathematics 10.2 (2012): 411-425. <http://eudml.org/doc/269059>.

@article{GiovanniCalvaruso2012,
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.},
author = {Giovanni Calvaruso},
journal = {Open Mathematics},
keywords = {Harmonic vector fields; Harmonic maps; Tangent sphere bundle; Generalized symmetric spaces; Pseudo-Riemannian homogeneous spaces; harmonic vector field; harmonic map; generalized symmetric spaces; pseudo-Riemannian space},
language = {eng},
number = {2},
pages = {411-425},
title = {Harmonicity of vector fields on four-dimensional generalized symmetric spaces},
url = {http://eudml.org/doc/269059},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Giovanni Calvaruso
TI - Harmonicity of vector fields on four-dimensional generalized symmetric spaces
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 411
EP - 425
AB - 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.
LA - eng
KW - Harmonic vector fields; Harmonic maps; Tangent sphere bundle; Generalized symmetric spaces; Pseudo-Riemannian homogeneous spaces; harmonic vector field; harmonic map; generalized symmetric spaces; pseudo-Riemannian space
UR - http://eudml.org/doc/269059
ER -

References

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