Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Ricci solitons on compact Kähler surfaces


Author: Thomas Ivey
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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, https://doi.org/10.1090/conm/071/954419
  • [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, https://doi.org/10.1016/0926-2245(93)90008-O
  • [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, https://doi.org/10.1215/S0012-7094-93-07224-9

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C20, 53C21

Retrieve articles in all journals with MSC (1991): 53C20, 53C21


Additional Information

Thomas Ivey
Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106-7058
Email: txi4@po.cwru.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03624-1
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