On a class of compact and non-compact quasi-Einstein metrics and their renormalizability properties Original Research Article

We construct a family of Kählerian quasi-Einstein metrics with an isometry group U(n) acting linearly on the holomorphic coordinates. Suitable restrictions on the parameters give rise to complete non-compact as well as compact metrics whose geometrical structure is studied in detail. The two-loop renormalizability properties are discussed according to whether one considers the bosonic σ-models or their (2,2) supersymmetric extension.