Bando, Shigetoshi; Mabuchi, Toshiki Uniqueness of Einstein Kähler metrics modulo connected group actions. (English) Zbl 0641.53065 Algebraic geometry, Proc. Symp., Sendai/Jap. 1985, Adv. Stud. Pure Math. 10, 11-40 (1987). [For the entire collection see Zbl 0628.00007.] The main purpose of this paper is to prove the uniqueness of Einstein Kähler metrics on an arbitrary compact complex manifold X with positive first Chern class \(c_ 1(X)_ R>0\) up to G-action. Such uniqueness was known only for: i) Kähler C-spaces [see Y. Matsushima, Nagoya Math. J. 46, 161-173 (1972; Zbl 0249.53050)] and ii) some non- homogeneous Einstein manifolds - recently discovered by Y. Sakane [see Examples of compact Einstein Kähler manifolds with positive Ricci tensor, Osaka J. Math. (to appear)]. Reviewer: B.N.Apanasov Cited in 8 ReviewsCited in 109 Documents MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:Einstein Kähler metrics; compact complex manifold; Chern class Citations:Zbl 0628.00007; Zbl 0249.53050 PDFBibTeX XML