Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces G 2 and G 2 / S O ( 4 )

László Verhóczki

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2012)

  • Volume: 51, Issue: 1, page 101-109
  • ISSN: 0231-9721

Abstract

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The exceptional compact symmetric spaces G 2 and G 2 / S O ( 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.

How to cite

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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 51.1 (2012): 101-109. <http://eudml.org/doc/246803>.

@article{Verhóczki2012,
abstract = {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.},
author = {Verhóczki, László},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {harmonic unit vector field; minimal unit vector field; Lie group; Riemannian symmetric space; isometric action; Riemannian symmetric space; harmonic unit vector field; minimal unit vector field; isometric action},
language = {eng},
number = {1},
pages = {101-109},
publisher = {Palacký University Olomouc},
title = {Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces $G_2$ and $G_2/SO(4)$},
url = {http://eudml.org/doc/246803},
volume = {51},
year = {2012},
}

TY - JOUR
AU - Verhóczki, László
TI - Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces $G_2$ and $G_2/SO(4)$
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2012
PB - Palacký University Olomouc
VL - 51
IS - 1
SP - 101
EP - 109
AB - 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.
LA - eng
KW - harmonic unit vector field; minimal unit vector field; Lie group; Riemannian symmetric space; isometric action; Riemannian symmetric space; harmonic unit vector field; minimal unit vector field; isometric action
UR - http://eudml.org/doc/246803
ER -

References

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  9. Verhóczki, L., 10.1007/s00605-002-0036-8, Monatsh. Math. 141 (2004), 323–335. (2004) Zbl1058.53041MR2053657DOI10.1007/s00605-002-0036-8
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