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An Equivariant Version of the K-energy

An Equivariant Version of the K-energy
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摘要 In this note, we present a connection between equivariant Bott–Chern classesand K?hler–Ricci solitons. We also propose a generalized version the of the K–energy. In this note, we present a connection between equivariant Bott–Chern classesand K?hler–Ricci solitons. We also propose a generalized version the of the K–energy.
作者 GangTIAN
机构地区 DepartmentofMathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第1期1-8,共8页 数学学报（英文版）
基金 Supported partially by NSF grants and a Simons fund
关键词 Kahler–Ricci soliton Bott–Chern class K–energy Kahler–Ricci soliton Bott–Chern class K–energy
分类号 O174.5 [理学—基础数学]
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参考文献9

  • 1Bott, R., Chern, S. S.: Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections. Acta Math., 114, 71-112 (1965).
  • 2Bismut, J-M.: Equivariant Bott-Chern currents and the Ray-Singer analytic torsion. Math. Ann., 287,495-507 (1990).
  • 3Donaldson, S.: Anti-self-dual Yang-Mills connections over complex surfaces and stable vector bundles. Proc.London Math. Soc.. 50. 1-26 (1985).
  • 4Futaki, A., Morita, S.: Invariant polynomials on compact complex manifolds. Proc. Japan Acad. Set. A,Math. Sci., 60, 369-372 (1984).
  • 5Tian, G., Zhu, X. H.: A new holomorphic invariant and uniqueness of Kahler-Ricci solitons. Comment.Math. Helv., 77, 297-325 (2002).
  • 6Mabuchi, T.: K-energy maps integrating Futaki invariants. Tohoku Math. J., 38, 245-257 (1986).
  • 7Tian, G.: Kahler-Einstein metrics with positive scalar curvature. Invent. Math.,130, 1-39 (1997).
  • 8Tian, G.: The K-energy on Hypersurfaces and Stability. Communications in Geometry and Analysis, 2,239-265 (1994).
  • 9Tian, G., Zhu, X. H.: Uniqueness of Kaihler-Ricci solitons. Acta Math., 184, 271-305 (2000).
Acta Mathematica Sinica,English Series
2005年 第1期

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