Volume 15, Issue 1 (4-2020)                   IJMSI 2020, 15(1): 65-78 | Back to browse issues page


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Aryanejad Y. Harmonicity and Minimality of Vector Fields on Lorentzian Lie Groups. IJMSI. 2020; 15 (1) :65-78
URL: http://ijmsi.ir/article-1-809-en.html
Abstract:  

‎We consider four-dimensional lie groups equipped with‎ ‎left-invariant Lorentzian Einstein metrics‎, ‎and determine the harmonicity properties ‎of vector fields on these spaces‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional ‎restricted to vector fields‎. ‎We also classify vector fields defining harmonic maps‎, ‎and calculate explicitly the energy of these vector ‎fields‎. ‎Then we study the minimality of critical points for the energy functional‎.

Type of Study: Research paper | Subject: General

References
1. A. R. Ashrafi, M. R. Ahmadi, Symmetry of fullerene C60, Iranian Journal of Mathematical Sciences and Informatics, 1(1), (2006) 1-13.
2. L. Bérard-Bérgery, Homogeneous Riemannian spaces of dimension four, Seminar A.Besse, Four-dimensional Riemannian geometry, (1985).
3. G. Calvaruso, Harmonicity properties of invariant vector fields on three-dimensional Lorentzian Lie groups, J.Geom. Phys. 61 (2011), 498-515. [DOI:10.1016/j.geomphys.2010.11.001]
4. G. Calvaruso and A. Zaeim, Four-dimensional Lorentzian Lie groups, Differ. Geom. Appl. 31 (2013), 496-509. [DOI:10.1016/j.difgeo.2013.04.006]
5. M. Chaichi, E. Garcia-Rio, Y. Matsushita, Curvature properties of four-dimensional Walker metrics, Classical Quantum Gravity, 22(3), (2005), 559-577. [DOI:10.1088/0264-9381/22/3/008]
6. M. Chaichi, E. Garcia-Rio, Y. Matsushita, Three-dimensional Lorentz manifolds admitting a parallel null vector field, J. Phys. A, 38(4), (2005), 841-850. [DOI:10.1088/0305-4470/38/4/005]
7. M. Dabirian, A. Iranmanesh, The molecular symmetry group theory of trimethylamine-BH3 addend (BH3 free of rotation), Iranian Journal of Mathematical Sciences and Informatics, 1(1), (2006) 15-26.
8. S. Dragomir, D. Perrone, Harmonic Vector Fields: Variational Principles and Differential Geometry, Elsevier, Science Ltd, (2011). [DOI:10.1016/B978-0-12-415826-9.00002-X]
9. O. Gil-Medrano, Relationship between volume and energy of vector fields, Diff. Geom. Appl. 15 (2001), 137-152. [DOI:10.1016/S0926-2245(01)00053-5]
10. T. Ishihara, Harmonic sections of tangent bundles, J. Math. Tokushima Univ. 13, (1979), 23-27.
11. O. Nouhaud, Applications harmoniques d'une variété riemannienne dans son fibré tangent, Généralisation, C. R. Acad. Sci. Paris Sér. A-B, 284(14), (1977), A815-A818.
12. A. Zaeim, M. Chaichi, Y. Aryanejad, On Lorentzian Two-Symmetric Manifolds of Dimension-Four, Iranian Journal of Mathematical Sciences and Informatics, 12(4), (2017) 81-94.

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