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

‎ 10.29252/ijmsi.15.1.65

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Harmonicity and Minimality of Vector Fields on Lorentzian Lie Groups
Y. Aryanejad
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.

Keywords: Harmonic vector fields‎, ‎Harmonic maps‎, ‎Einstein metrics‎, ‎Lie group‎, ‎Pseudo-Riemannian homogeneous spaces.
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Type of Study: Research paper | Subject: General
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