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Isotropic almost complex structures and harmonic unit vector fields

Amir Baghban; Esmaeil Abedi

Archivum Mathematicum (2018)

  • Volume: 054, Issue: 1, page 15-32
  • ISSN: 0044-8753

Abstract

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Isotropic almost complex structures J δ , σ define a class of Riemannian metrics g δ , σ on tangent bundles of Riemannian manifolds which are a generalization of the Sasaki metric. In this paper, some results will be obtained on the integrability of these almost complex structures and the notion of a harmonic unit vector field will be introduced with respect to the metrics g δ , 0 . Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained.

How to cite

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Baghban, Amir, and Abedi, Esmaeil. "Isotropic almost complex structures and harmonic unit vector fields." Archivum Mathematicum 054.1 (2018): 15-32. <http://eudml.org/doc/294268>.

@article{Baghban2018,
abstract = {Isotropic almost complex structures $J_\{\delta , \sigma \}$ define a class of Riemannian metrics $g_\{\delta , \sigma \}$ on tangent bundles of Riemannian manifolds which are a generalization of the Sasaki metric. In this paper, some results will be obtained on the integrability of these almost complex structures and the notion of a harmonic unit vector field will be introduced with respect to the metrics $g_\{\delta , 0\}$. Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained.},
author = {Baghban, Amir, Abedi, Esmaeil},
journal = {Archivum Mathematicum},
keywords = {complex structures; energy functional; isotropic almost complex structure; unit tangent bundle; variational problem; tension field},
language = {eng},
number = {1},
pages = {15-32},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Isotropic almost complex structures and harmonic unit vector fields},
url = {http://eudml.org/doc/294268},
volume = {054},
year = {2018},
}

TY - JOUR
AU - Baghban, Amir
AU - Abedi, Esmaeil
TI - Isotropic almost complex structures and harmonic unit vector fields
JO - Archivum Mathematicum
PY - 2018
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 054
IS - 1
SP - 15
EP - 32
AB - Isotropic almost complex structures $J_{\delta , \sigma }$ define a class of Riemannian metrics $g_{\delta , \sigma }$ on tangent bundles of Riemannian manifolds which are a generalization of the Sasaki metric. In this paper, some results will be obtained on the integrability of these almost complex structures and the notion of a harmonic unit vector field will be introduced with respect to the metrics $g_{\delta , 0}$. Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained.
LA - eng
KW - complex structures; energy functional; isotropic almost complex structure; unit tangent bundle; variational problem; tension field
UR - http://eudml.org/doc/294268
ER -

References

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  4. Aguilar, R.M., 10.1007/BF02568316, Manuscripta Math. 90 (1996), 429–436. (1996) MR1403714DOI10.1007/BF02568316
  5. Baghban, A., Abedi, E., On the harmonic vector fields, th Seminar on Geometry and Topology, Amirkabir University of Technology, 2015. (2015) 
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  8. Calvaruso, G., 10.2478/s11533-011-0109-9, Central Eur. J. Math. 10 (2012), 411–425. (2012) MR2886549DOI10.2478/s11533-011-0109-9
  9. Dragomir, S., Perrone, D., Harmonic vector fields, Variational Principles and Differential Geometry, Elsevier, 2012. (2012) MR3286434
  10. Friswell, R.M., Harmonic vector fields on pseudo-Riemannian manifolds, Ph.D. thesis, 2014. (2014) 
  11. Friswell, R.M., Wood, C.M., 10.1016/j.geomphys.2016.10.015, J. Geom. Phys. 112 (2017), 45–58. (2017) MR3588756DOI10.1016/j.geomphys.2016.10.015
  12. Gil-Medrano, O., 10.1016/S0926-2245(01)00053-5, Differential Geom. Appl. 15 (2001), 137–152. (2001) MR1857559DOI10.1016/S0926-2245(01)00053-5
  13. Sasaki, S., 10.2748/tmj/1178244668, Tôhoku Math. J. 10, 338–354. MR0112152DOI10.2748/tmj/1178244668
  14. Urakawa, H., Calculus of variations and harmonic maps, American Mathematical Society, 1993. (1993) MR1252178

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