Proceedings of the Japan Academy, Series A, Mathematical Sciences

Some invariant and equivariant cohomology classes of the space of Kähler metrics

Akito Futaki

Full-text: Open access

Abstract

Invariant and equivariant cohomology classes on the space of Kähler forms are defined. Relations to the obstructions to the existence of Kähler-Einstein metrics and Kähler metrics of harmonic Chern forms are discussed.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 3 (2002), 27-29.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392745

Digital Object Identifier
doi:10.3792/pjaa.78.27

Mathematical Reviews number (MathSciNet)
MR1894896

Zentralblatt MATH identifier
1017.53061

Subjects
Primary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 55N91: Equivariant homology and cohomology [See also 19L47]

Keywords
Kähler forms invariant cohomology equivariant cohomology Hermitian multiplier structure Kähler-Einstein metric

Citation

Futaki, Akito. Some invariant and equivariant cohomology classes of the space of Kähler metrics. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 3, 27--29. doi:10.3792/pjaa.78.27. https://projecteuclid.org/euclid.pja/1148392745


Export citation

References

  • Bando, S.: An obstruction for Chern class forms to be harmonic (1983). (Preprint).
  • Bando, S., and Mabuchi, T.: On some integral invariants on complex manifolds. I. Proc. Japan Acad., 62A, 197–200 (1986).
  • Bourguignon, J. P.: Invariants Intégraux Fonctionnels pour des Équations dérivées Partielles d'origine Géométrique. Lecture Notes in Math. no. 1209, Springer, Heidelberg-Tokyo (1986).
  • Bott, R., and Tu, L.: Equivariant characteristic classes in the Cartan model (math.DG/0102001).
  • Calabi, E.: Extremal Kähler metrics II. Differential Geometry and Complex Analysis (eds. Chavel, I., and Farkas, H. M.). Springer, Heidelberg-Tokyo, pp. 95–114 (1985).
  • Fujiki, A.: On automorphism groups of compact Kähler manifolds. Invent. Math., 44, 225–258 (1978).
  • Futaki, A.: An obstruction to the existence of Einstein Kähler metrics. Invent. Math., 73, 437–443 (1983).
  • Futaki, A.: On compact Kähler manifolds of constant scalar curvature. Proc. Japan Acad., 59A, 401–402 (1983).
  • Futaki, A.: Kähler-Einstein Metrics and Integral Invariants. Lecture Notes in Math. no. 1314, Springer, Heidelberg-Tokyo (1988).
  • Futaki, A., and Nakagawa, Y.: Characters of automorphism groups associated with Kähler classes and functionals with cocycle conditions. Kodai Math. J., 24, 1–14 (2001).
  • Guillemin, V., and Sternberg, S.: Supersymmetry and Equivariant de Rham Theory. Springer, Heidelberg-Tokyo (1999).
  • Mabuchi, T.: Kähler-Einstein metrics for manifolds with nonvanishing Futaki character. Tohoku Math. J., 53, 171–182 (2001).
  • Mabuchi, T.: Multiplier Hermitian strucures on Kähler manifolds (preprint).
  • Tian, G., and Zhu, X. H.: Uniqueness of Kähler-Ricci solitons. Acta Math., 184, 271–305 (2000).
  • Warner, F. W.: Foundations of differentiable manifolds and Lie groups. Graduate Texts in Math. vol. 94, Springer, Heidelberg-Tokyo (1971).