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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Existence of extremal metrics on compact almost homogeneous Kähler manifolds with two ends
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by Daniel Guan PDF
Trans. Amer. Math. Soc. 347 (1995), 2255-2262 Request permission


In this note we prove the existence and the uniqueness of extremal metrics in every Kähler class of any compact almost homogeneous Kähler manifold with two ends by considering the scalar curvature equations, those manifolds might not be projective. We also prove that there are extremal metrics in some Kähler classes of a completion of the multicanonical line bundle of a Kähler-Einstein manifold of positive Ricci curvature.
  • D. Burns and P. De Bartolomeis, Stability of vector bundles and extremal metrics, Invent. Math. 92 (1988), no. 2, 403–407. MR 936089, DOI 10.1007/BF01404460
  • Eugenio Calabi, Extremal Kähler metrics, Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, N.J., 1982, pp. 259–290. MR 645743
  • Eugenio Calabi, Extremal Kähler metrics. II, Differential geometry and complex analysis, Springer, Berlin, 1985, pp. 95–114. MR 780039
  • Josef Dorfmeister and Zhuang Dan Guan, Fine structure of reductive pseudo-Kählerian spaces, Geom. Dedicata 39 (1991), no. 3, 321–338. MR 1123147, DOI 10.1007/BF00150759
  • A. Futaki, T. Mabuchi, and Y. Sakane, Einstein-Kähler metrics with positive Ricci curvature, Kähler metric and moduli spaces, Adv. Stud. Pure Math., vol. 18, Academic Press, Boston, MA, 1990, pp. 11–83. MR 1145246, DOI 10.2969/aspm/01820011
  • Z. Guan, On certain complex manifolds, Dissertation, Univ. of California, Berkeley, CA, 1993.
  • Daniel Zhuang-Dan Guan, Quasi-Einstein metrics, Internat. J. Math. 6 (1995), no. 3, 371–379. MR 1327154, DOI 10.1142/S0129167X95000110
  • —, Quasi-Einstein metrics and evolution of metrics in a Kähler class. I, in preparation.
  • Alan T. Huckleberry and Dennis M. Snow, Almost-homogeneous Kähler manifolds with hypersurface orbits, Osaka Math. J. 19 (1982), no. 4, 763–786. MR 687772
  • A. Hwang, Extremal Kähler metrics on almost-homogeneous spaces, preprint, 1992.
  • Norihito Koiso, On rotationally symmetric Hamilton’s equation for Kähler-Einstein metrics, Recent topics in differential and analytic geometry, Adv. Stud. Pure Math., vol. 18, Academic Press, Boston, MA, 1990, pp. 327–337. MR 1145263, DOI 10.2969/aspm/01810327
  • Norihito Koiso and Yusuke Sakane, Nonhomogeneous Kähler-Einstein metrics on compact complex manifolds, Curvature and topology of Riemannian manifolds (Katata, 1985) Lecture Notes in Math., vol. 1201, Springer, Berlin, 1986, pp. 165–179. MR 859583, DOI 10.1007/BFb0075654
  • —, Non-homogeneous Kähler-Einstein metrics on compact complex manifolds. II, Osaka J. Math. 25 (1988), 933-959.
  • Marc Levine, A remark on extremal Kähler metrics, J. Differential Geom. 21 (1985), no. 1, 73–77. MR 806703
  • Toshiki Mabuchi, Einstein-Kähler forms, Futaki invariants and convex geometry on toric Fano varieties, Osaka J. Math. 24 (1987), no. 4, 705–737. MR 927057
  • Yusuke Sakane, Examples of compact Einstein Kähler manifolds with positive Ricci tensor, Osaka J. Math. 23 (1986), no. 3, 585–616. MR 866267
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 2255-2262
  • MSC: Primary 58E11; Secondary 53C25, 53C55
  • DOI:
  • MathSciNet review: 1285992