Quasi-Einstein Kähler metrics
The authors write an ansatz for quasi-Einstein Kähler metrics (also called Kähler Ricci solitons) and construct new examples on complex line bundles (or their compactifications \({\mathbf P}(\mathcal{O}\otimes L)\)) over Kähler-Einstein base manifolds \(B\). Firstly, the authors obtain in Sect. 2 an ansatz for quasi-Einstein Kähler metrics with a torus symmetry, that is used to find solutions in the case of \({\mathbf S}^1\) symmetry. Finally they construct new compact generalized quasi-Einstein Kähler metrics on some ruled surfaces, including some of the Guan examples as special cases [\textit{Z. D. Guan}, Int. J. Math. 6, 371-379 (1995; Zbl 0847.53032)] as well as some metrics already constructed by \textit{N. Koiso} [Adv. Stud. Pure Math. 18-I, 327-337 (1999; Zbl 0739.53052)].
scientific article; zbMATH DE number 1508184