Type I Almost-Homogeneous Manifolds of Cohomogeneity One-II

• Published in: Pacific journal of applied mathematics Vol. 3; no. 3; p. 181
• Main Author: Guan, Daniel
• Format: Journal Article
• Language: English
• Published: Hauppauge Nova Science Publishers, Inc 01.07.2011
• Subjects: Bundles; Classification; Constants; Joining; Manifolds; Mathematical analysis; Mathematics; Scalars; Series & special reports; Uniqueness
• ISSN: 1941-3963

This is the second part of [Gu1] on the existence of Kähler Einstein metrics of the general type I almost homogeneous manifolds of cohomogeneity one. We actually carry out all the results in [Gu3] to the type I cases. We also prove the existence of smooth geodesic connecting any two given metrics on the Mabuchi moduli space of Kähler metrics, which leads to the uniqueness of our Kähler metrics with constant scalar curvatures if they exist. We obtain a lot of new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. Furthermore, in this paper we also deal with the cases with a higher codimensional end, then obtain more Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metric. As an offshot, we are able to classify compact Kähler manifolds which are almost homogeneous of cohomogeneity one with a higher codimensional end. With applying our results to the canonical circle bundles we also obtain Sasakian manifolds with or without Sasakian-Einstein metrics. That also give some open Calabi-Yau manifolds.