Duke Mathematical Journal

Metrics with nonnegative isotropic curvature

Mario J. Micallef and McKenzie Y. Wang

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Article information

Source
Duke Math. J. Volume 72, Number 3 (1993), 649-672.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077289625

Mathematical Reviews number (MathSciNet)
MR1253619

Zentralblatt MATH identifier
0804.53058

Digital Object Identifier
doi:10.1215/S0012-7094-93-07224-9

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Citation

Micallef, Mario J.; Wang, McKenzie Y. Metrics with nonnegative isotropic curvature. Duke Math. J. 72 (1993), no. 3, 649--672. doi:10.1215/S0012-7094-93-07224-9. http://projecteuclid.org/euclid.dmj/1077289625.


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References

  • [Bg1] M. Berger, Sur quelques variétés riemanniennes suffisamment pincées, Bull. Soc. Math. France 88 (1960), 57–71.
  • [Bg2] M. Berger, Pincement riemannien et pincement holomorphe, Ann. Scuola Norm. Sup. Pisa (3) 14 (1960), 151–159.
  • [Bg3] M. Berger, Sur les variétés à opérateur de courbure positif, C. R. Acad. Sci.Ser. Paris 253 (1961), 2832–2834.
  • [Bg4] M. Berger, Sur quelques variétés d'Einstein compactes, Ann. Mat. Pura Appl. (4) 53 (1961), 89–95.
  • [Be] A. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987.
  • [Bo] J. P. Bourguignon, Les variétés de dimension $4$ à signature non nulle dont la courbure est harmonique sont d'Einstein, Invent. Math. 63 (1981), no. 2, 263–286.
  • [D] A. Derdzinski, Self-dual Kähler manifolds and Einstein manifolds of dimension four, Compositio Math. 49 (1983), no. 3, 405–433.
  • [GK] S. Goldberg and S. Kobayashi, Holomorphic bisectional curvature, J. Differential Geometry 1 (1967), 225–233.
  • [GrL] M. Gromov and H. B. Lawson, The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. (2) 111 (1980), no. 3, 423–434.
  • [H1] R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255–306.
  • [H2] R. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), no. 2, 153–179.
  • [He] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1978.
  • [Hi] N. Hitchin, Compact four-dimensional Einstein manifolds, J. Differential Geometry 9 (1974), 435–441.
  • [K] S. Kobayashi, On compact Kähler manifolds with positive definite Ricci tensor, Ann. of Math. (2) 74 (1961), 570–574.
  • [KN] S. Kobayashi and K. Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969.
  • [LMs] H. B. Lawson and M. L. Michelsohn, Spin geometry, Princeton Mathematical Series, vol. 38, Princeton University Press, Princeton, NJ, 1989.
  • [Le] C. LeBrun, On the topology of self-dual $4$-manifolds, Proc. Amer. Math. Soc. 98 (1986), no. 4, 637–640.
  • [MMr] M. Micallef and J. D. Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. of Math. (2) 127 (1988), no. 1, 199–227.
  • [MWo] M. Micallef and J. Wolfson, The second variation of area of minimal surfaces in four-manifolds, Math. Ann. 295 (1993), no. 2, 245–267.
  • [MnR] Min-Oo Maung and E. Ruh, Curvature deformations, Curvature and topology of Riemannian manifolds (Katata, 1985), Lecture Notes in Math., vol. 1201, Springer, Berlin, 1986, pp. 180–190.
  • [P] A. Polombo, De nouvelles formules de Weitzenböck pour des endomorphismes harmoniques. Applications géométriques, Ann. Sci. École Norm. Sup. (4) 25 (1992), no. 4, 393–428.
  • [SY1] R. Schoen and S.-T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), no. 1-3, 159–183.
  • [SY2] R. Schoen and S.-T. Yau, Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math. 92 (1988), no. 1, 47–71.
  • [Se] W. Seaman, On manifolds with nonnegative curvature on totally isotropic 2-planes, Trans. Amer. Math. Soc. 338 (1993), no. 2, 843–855.
  • [T] G. Tian, On Calabi's conjecture for complex surfaces with positive first Chern class, Invent. Math. 101 (1990), no. 1, 101–172.
  • [W] J. A. Wolf, Spaces of constant curvature, Publish or Perish Inc., Boston, Mass., 1977.
  • [Y1] S.-T. Yau, On the curvature of compact Hermitian manifolds, Invent. Math. 25 (1974), 213–239.
  • [Y2] S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math. 31 (1978), no. 3, 339–411.