On the geometry of some solvable extensions of the Heisenberg group
Mehri Nasehi, Mansour Aghasi (2018)
Czechoslovak Mathematical Journal
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In this paper we first classify left-invariant generalized Ricci solitons on some solvable extensions of the Heisenberg group in both Riemannian and Lorentzian cases. Then we obtain the exact form of all left-invariant unit time-like vector fields which are spatially harmonic. We also calculate the energy of an arbitrary left-invariant vector field on these spaces and obtain all vector fields which are critical points for the energy functional restricted to vector fields of the same...