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Ricci solitons on compact Kähler surfaces

Author: Thomas Ivey
Journal: Proc. Amer. Math. Soc. 125 (1997), 1203-1208
MSC (1991): Primary 53C20, 53C21
MathSciNet review: 1353388
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Abstract: We classify the Kähler metrics on compact manifolds of complex dimension two that are solitons for the constant-volume Ricci flow, assuming that the curvature is slightly more positive than that of the single known example of a soliton in this dimension.

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  • [C] H. D. Cao, Existence of gradient Ricci-Kähler solitons, preprint (1994).
  • [F] T. Frankel, Manifolds with positive curvature, Pacific J. Math. 11 (1961), 165-174. MR 23a:600
  • [G] P. Gauduchon, Surfaces Kähleriennes dont la courbure admet certaines conditions de positivité, in ``Géométrie riemannienne en dimension 4'', Cedic, Fernand Nathan, Paris (1981). CMP 17:05
  • [H1] Richard S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255–306. MR 664497
  • [H2] Richard S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), no. 2, 153–179. MR 862046
  • [H3] Richard S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity (Santa Cruz, CA, 1986) Contemp. Math., vol. 71, Amer. Math. Soc., Providence, RI, 1988, pp. 237–262. MR 954419,
  • [H4] -, The formation of singularities in the Ricci flow, preprint (1994).
  • [H5] -, Four-manifolds with positive isotropic curvature, Surveys in Differential Geometry, Vol. II, International Press, 1995.
  • [I1] T. Ivey, On solitons for the Ricci flow, Ph.D. thesis, Duke University (1992).
  • [I2] Thomas Ivey, Ricci solitons on compact three-manifolds, Differential Geom. Appl. 3 (1993), no. 4, 301–307. MR 1249376,
  • [K] 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
  • [MW] Mario J. Micallef and McKenzie Y. Wang, Metrics with nonnegative isotropic curvature, Duke Math. J. 72 (1993), no. 3, 649–672. MR 1253619,

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Additional Information

Thomas Ivey
Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106-7058

Keywords: Ricci flow, solitons, K\"ahler surfaces
Received by editor(s): July 26, 1995
Received by editor(s) in revised form: October 24, 1995
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society