Invariant harmonic unit vector fields on the oscillator groups

Na Xu; Ju Tan

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 4, page 907-924
  • ISSN: 0011-4642

Abstract

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We find all the left-invariant harmonic unit vector fields on the oscillator groups. Besides, we determine the associated harmonic maps from the oscillator group into its unit tangent bundle equipped with the associated Sasaki metric. Moreover, we investigate the stability and instability of harmonic unit vector fields on compact quotients of four dimensional oscillator group G 1 ( 1 ) .

How to cite

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Xu, Na, and Tan, Ju. "Invariant harmonic unit vector fields on the oscillator groups." Czechoslovak Mathematical Journal 69.4 (2019): 907-924. <http://eudml.org/doc/294707>.

@article{Xu2019,
abstract = {We find all the left-invariant harmonic unit vector fields on the oscillator groups. Besides, we determine the associated harmonic maps from the oscillator group into its unit tangent bundle equipped with the associated Sasaki metric. Moreover, we investigate the stability and instability of harmonic unit vector fields on compact quotients of four dimensional oscillator group $G_1(1)$.},
author = {Xu, Na, Tan, Ju},
journal = {Czechoslovak Mathematical Journal},
keywords = {harmonic vector field; harmonic map; oscillator group},
language = {eng},
number = {4},
pages = {907-924},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Invariant harmonic unit vector fields on the oscillator groups},
url = {http://eudml.org/doc/294707},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Xu, Na
AU - Tan, Ju
TI - Invariant harmonic unit vector fields on the oscillator groups
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 907
EP - 924
AB - We find all the left-invariant harmonic unit vector fields on the oscillator groups. Besides, we determine the associated harmonic maps from the oscillator group into its unit tangent bundle equipped with the associated Sasaki metric. Moreover, we investigate the stability and instability of harmonic unit vector fields on compact quotients of four dimensional oscillator group $G_1(1)$.
LA - eng
KW - harmonic vector field; harmonic map; oscillator group
UR - http://eudml.org/doc/294707
ER -

References

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