A Splitting Theorem for Extremal K?hler Metrics

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• 作者：Vestislav Apostolov ; Hongnian Huang
• 关键词：K?hler geometry ; Extremal metrics ; Chow stability ; 53C55
• 刊名：Journal of Geometric Analysis
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：25
• 期：1
• 页码：149-170
• 全文大小：422 KB
• 参考文献：1. Apostolov, V., Calderbank, D.M.J., Gauduchon, P., T?nnesen-Friedman, C.: Hamiltonian 2-forms in K?hler geometry, III. Extremal metrics and stability. Invent. Math. 173, 547-01 (2008) CrossRef
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  5. Calabi, E.: Extremal K?hler metrics, II. In: Chavel, I., Farkas, H.M. (eds.) Differential Geometry and Complex Analysis. Springer, Berlin (1985)
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  11. Donaldson, S.K.: Scalar curvature and projective embeddings, I. J. Differ. Geom. 59, 479-22 (2001)
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  13. Donaldson, S.K.: Conjectures in K?hler geometry. In: Strings and Geometry. Clay Math. Proc., vol.?3, pp. 71-8. AMS, Providence (2004)
  14. Donaldson, S.K.: Scalar curvature and projective embeddings. II. Q. J. Math. 56, 345-56 (2005) CrossRef
  15. Donaldson, S.K.: Lower bounds on the Calabi functional. J. Differ. Geom. 70, 453-72 (2005)
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  19. Huang, H., Zheng, K.: The stability of the Calabi flow near an extremal metric. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 11, 167-75 (2012)
  20. Gauduchon, P.: Fibrés hermitiens à endomorphisme de Ricci non-négatif. Bull. Soc. Math. Fr. 105, 113-40 (1977)
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

Based on recent work of S.K.?Donaldson (J. Differ. Geom. 59:479-22, 2001; Q. J. Math. 56:345-56, 2005) and T.?Mabuchi (Osaka J. Math. 41:563-82, 2004; Invent. Math. 159:225-43, 2005; Osaka J. Math. 46:115-39, 2009), we prove that any extremal K?hler metric in the sense of E.?Calabi?(in Seminar on Differential Geometry, pp. 259-90. Princeton Univ. Press, Princeton, 1982), defined on the product of polarized compact complex projective manifolds is the product of extremal K?hler metrics on each factor, provided that either the polarized manifold is asymptotically Chow semi-stable or its automorphism group satisfies a constraint. This extends a result of S.-T.?Yau (Commun. Anal. Geom. 1:473-86, 1993) about the splitting of a K?hler–Einstein metric on the product of compact complex manifolds to the more general setting of extremal K?hler metrics.