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)

 
 

 

A new proof of Mok's generalized Frankel conjecture theorem


Author: Hui-Ling Gu
Journal: Proc. Amer. Math. Soc. 137 (2009), 1063-1068
MSC (2000): Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-08-09611-1
Published electronically: October 15, 2008
MathSciNet review: 2457447
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this short paper, we will give a simple and transcendental proof for Mok's theorem of the generalized Frankel conjecture. This work is based on the maximum principle proposed by Brendle and Schoen.


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

  • 1. S. Bando, On the classification of three-dimensional compact Kähler manifolds of nonnegative bisectional curvature, J. Diff. Geom. 19, (1984), 283-297. MR 755227 (86i:53042)
  • 2. S. Brendle and R. Schoen, Manifolds with $ 1/4$-pinched curvature are space forms, arXiv:math.DG/0705.0766 v2 May 2007.
  • 3. S. Brendle and R. Schoen, Classification of manifolds with weakly $ 1/4$-pinched curvatures, arXiv:math.DG/0705.3963 v1 May 2007.
  • 4. H. D. Cao and B. Chow, Compact Kähler manifolds with nonnegative curvature operator, Invent. Math. 83 (1986), 553-556. MR 827367 (87h:53095)
  • 5. R. S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), 153-179. MR 862046 (87m:53055)
  • 6. R. S. Hamilton, The formation of singularities in the Ricci flow, Surveys in Differential Geometry (Cambridge, MA, 1993), 2, 7-136, International Press, Cambridge, MA, 1995. MR 1375255 (97e:53075)
  • 7. A. Howard, B. Smyth, and H. Wu, On compact Kähler manifolds of nonnegative bisectional curvature, I, Acta Math. 147 (1981), 51-56. MR 631087 (83e:53064a)
  • 8. N. Mok, The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature, J. Diff. Geom. 27 (1988), 179-214. MR 925119 (89d:53115)
  • 9. S. Mori, Projective manifolds with ample tangent bundles, Ann. of Math. (2) 110 (1979), 593-606. MR 554387 (81j:14010)
  • 10. Y. T. Siu and S. T. Yau, Complex Kähler manifolds of positive bisectional curvature, Invent. Math. 59 (1980), 189-204. MR 577360 (81h:58029)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C20

Retrieve articles in all journals with MSC (2000): 53C20


Additional Information

Hui-Ling Gu
Affiliation: Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275 People’s Republic of China
Email: ghl1026@tom.com

DOI: https://doi.org/10.1090/S0002-9939-08-09611-1
Keywords: Generalized Frankel conjecture, holomorphic bisectional curvature, maximal principle
Received by editor(s): August 20, 2007
Received by editor(s) in revised form: April 5, 2008
Published electronically: October 15, 2008
Additional Notes: The author was supported in part by NSFC 10428102 and NKBRPC 2006CB805905.
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society