Double extensions on Riemannian Ricci nilsolitons
Riemannian Ricci solitons are a generalization of Einstein metrics and they were studied by many authors. In pseudo-Riemannian geometry, Einstein metrics are studied in many works. But there are not so many results about pseudo-Riemannian non-Einstein solitons. In the present paper, algebraic Lorentzian Ricci nilsolitons are studied. From a given algebraic Riemannian Ricci nilsoliton, by the process of double extension and using Lorentz data, a Lorentz Ricci nilsoliton in constructed. It is shown that all Lorentz Ricci nilsoliton with degenerate center arise this way. A possibility for classification of these nilsolitons arises. Some particular situations are considered in more detail and examples are given.
scientific article; zbMATH DE number 7389664
scientific article