Levine, Marc A remark on extremal Kähler metrics. (English) Zbl 0601.53056 J. Differ. Geom. 21, 73-77 (1985). It is known that Kähler-Einstein metrics on Kähler manifolds are solutions of a certain variational problem, introduced by Calabi. Calabi also proved that for such manifolds with extremal metrics the group of holomorphic automorphisms must contain a nontrivial compact real Lie subgroup, if it has positive dimension. The author constructs two manifolds which fail to have such a compact subgroup of their automorphism group; so these are examples of manifolds which do not have extremal metrics. Reviewer: V.Marenich Cited in 16 Documents MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:Kähler-Einstein metrics; Kähler manifolds; extremal metrics; holomorphic automorphisms PDFBibTeX XMLCite \textit{M. Levine}, J. Differ. Geom. 21, 73--77 (1985; Zbl 0601.53056) Full Text: DOI