Harmonicity and Minimality of Vector Fields on Lorentzian Lie Groups

Author(s):

Y. Aryanejad*

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:15 Issue: 1, May 2020
Pages:
65 to 78
https://www.magiran.com/p2127011