Abstract
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.
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