2016/11/20 by Dmitri V. Alekseevsky, Alekseevsky, Dmitri, Fabio Zuddas +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1611.06521
openalex publication_date 2016/11/20 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Let M be a cohomogeneity one manifold of a compact semisimple Lie group G with one singular orbit S0 = G/H. Then M is G- diffeomorphic to the total space G ×H V of the homogeneous vector bundle over S0 defined by a sphere transitive representation of G in a vector space V. We describe all such manifolds M which admit an invariant Kahler structure of standard type. This means that the restriction μ: S = Gx = G/L → F = G/K of the moment map of M to a regular orbit S = G/L is a holomorphic map of S with the induced CR structure onto a flag manifold F = G/K, where K = NG(L), endowed with an invariant complex structure JF . We describe all such standard Kahler cohomogeneity one manifolds in terms of the painted Dynkin diagram associated with (F=G/K; JF) and a parametrized interval in some T-Weyl chamber. We determine which of these manifolds admit invariant Kahler-Einstein metrics.