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A new proof of Mok's generalized Frankel conjecture theorem
Author(s):
Hui-Ling
Gu
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1063-1068.
MSC (2000):
Primary 53C20
Posted:
October 15, 2008
MathSciNet review:
2457447
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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:
-
- 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
 -pinched curvature are space forms, arXiv:math.DG/0705.0766 v2 May 2007. - 3.
- S. Brendle and R. Schoen, Classification of manifolds with weakly
 -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)
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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:
10.1090/S0002-9939-08-09611-1
PII:
S 0002-9939(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
Posted:
October 15, 2008
Additional Notes:
The author was supported in part by NSFC 10428102 and NKBRPC 2006CB805905.
Communicated by:
Richard A. Wentworth
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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