On semi-direct extensions of the Heisenberg group (Q2228320)

The author gives a systematic study of the semi-direct extensions of the three-dimensional Heisenberg group, equipped with a one-parameter family of left-invariant metrics. An explicit description of the semi-direct extension and Ricci solitons are discussed. The curvature properties of the semi-direct extensions are studied. He completely classifies Ricci solitons of metrics concerning the global coordinates and constructs new examples of non-algebraic Lorentzian Ricci solitons.