Abstract:This paper is one of a series in which we generalize our earlier results on the equivalence of existence of Calabi extremal metrics to the geodesic stability for any type I compact complex almost homogeneous manifolds of cohomogeneity one. In this paper, we actually carry all the earlier results to the type I cases. In Part II, we obtained a substantial amount of new Kähler–Einstein manifolds as well as Fano manifolds without Kähler–Einstein metrics. In particular, by applying Theorem 15 therein, we obtained c… Show more
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