Kahler manifolds with large isometry group

1997/08/31 by Fabio Podestà, Podesta', F., Andrea Spiro +1
Mathematics · #53C55 53C25 57S15 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.dg-ga/9709003

openalex publication_date 1997/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate compact Kahler manifolds, which are acted on by a semisimple compact Lie group G of isometries with one hypersurface orbit. In case of ordinary action and projectable complex structure, we set up a one to one correspondence between such manifolds and abstract models. The Ricci tensor is then computed and we fully characterize the Kahler-Einstein manifolds with an ordinary cohomogeneity one action and projectable complex structure.

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