Ricci solitons on compact Kähler surfaces
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- by Thomas Ivey
- Proc. Amer. Math. Soc. 125 (1997), 1203-1208
- DOI: https://doi.org/10.1090/S0002-9939-97-03624-1
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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.References
- H. D. Cao, Existence of gradient Ricci-Kähler solitons, preprint (1994).
- Morgan Ward, Note on the general rational solution of the equation $ax^2-by^2=z^3$, Amer. J. Math. 61 (1939), 788–790. MR 23, DOI 10.2307/2371337
- P. Gauduchon, Surfaces Kähleriennes dont la courbure admet certaines conditions de positivité, in “Géométrie riemannienne en dimension 4”, Cedic, Fernand Nathan, Paris (1981).
- Richard S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry 17 (1982), no. 2, 255–306. MR 664497
- Richard S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), no. 2, 153–179. MR 862046
- 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, DOI 10.1090/conm/071/954419
- —, The formation of singularities in the Ricci flow, preprint (1994).
- —, Four-manifolds with positive isotropic curvature, Surveys in Differential Geometry, Vol. II, International Press, 1995.
- T. Ivey, On solitons for the Ricci flow, Ph.D. thesis, Duke University (1992).
- Thomas Ivey, Ricci solitons on compact three-manifolds, Differential Geom. Appl. 3 (1993), no. 4, 301–307. MR 1249376, DOI 10.1016/0926-2245(93)90008-O
- 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, DOI 10.2969/aspm/01810327
- Mario J. Micallef and McKenzie Y. Wang, Metrics with nonnegative isotropic curvature, Duke Math. J. 72 (1993), no. 3, 649–672. MR 1253619, DOI 10.1215/S0012-7094-93-07224-9
Bibliographic Information
- Thomas Ivey
- Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106-7058
- MR Author ID: 333843
- Email: txi4@po.cwru.edu
- Received by editor(s): July 26, 1995
- Received by editor(s) in revised form: October 24, 1995
- Communicated by: Peter Li
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1203-1208
- MSC (1991): Primary 53C20, 53C21
- DOI: https://doi.org/10.1090/S0002-9939-97-03624-1
- MathSciNet review: 1353388