Skip to main content
SpringerLink
Log in

Moving Symplectic Curves in Kähler-Einstein Surfaces

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

We derive a parabolic equation for the Kähler angle of a real surface evolving under the mean curvature flow in a Kähler-Einstein surface and show that a symplectic curve remains symplectic with the flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R Wolfson. Minimal surfaces in Kähler surfaces and Ricci curvature. Jour Diff Geom, 1989, 29: 281–294

    MATH  MathSciNet  Google Scholar 

  2. J Y Chen, G Tian. Minimal surfaces in Riemannian 4-manifolds. GAFA, 1997, 7: 873–916

    Article  MATH  Google Scholar 

  3. S S Chern, RWolfson. Minimal surfaces by moving frames. Ann of Math, 1983, 105: 59–83

    MATH  MathSciNet  Google Scholar 

  4. R Wolfson. On minimal surfaces in a Kähler manifold of constant holomorphic sectional curvature. Trans AMS, 1985, 290(2): 627–646

    Article  MATH  MathSciNet  Google Scholar 

  5. R Hamilton. Monotonicity formulas for parabolic flows on manifolds. Comm Anal Geom, 1993, 1(1): 127–137

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The University of British Columbia, Vancouver, B. C. V6T 1Z2, Canada

    Jingyi Chen

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.

    Gang Tian

Authors
  1. Jingyi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gang Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jingyi Chen.

Additional information

Chen is supported partially by an Alfred P. Sloan Research Fellowship and a grant from NSERC

Tian is supported in part by a grant from NSF

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, J., Tian, G. Moving Symplectic Curves in Kähler-Einstein Surfaces. Acta Math Sinica 16, 541–548 (2000). https://doi.org/10.1007/s101140000075

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s101140000075

Keywords

1991MR Subject Classification

Search

Navigation