A new proof of Mok’s generalized Frankel conjecture theorem. (English) Zbl 1165.53024
Following Frankel’s conjecture and the works of K. Diederich and {J. E. Fornaess} [Ann. Math. (2) 110, 575–592 (1979; Zbl 0394.32012)] and Y.-T. Siu and S.-T. Yau [Invent. Math. 59, 189–204 (1980; Zbl 0442.53056)], the author considers a similar problem and gives a new proof of Mok’s generalized Frankel conjecture. This work is very interesting.
Reviewer: Peibiao Zhao (Nanjing)
MSC:
| 53C20 | Global Riemannian geometry, including pinching |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
| 53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
References:
| [1] | Shigetoshi Bando, On the classification of three-dimensional compact Kaehler manifolds of nonnegative bisectional curvature, J. Differential Geom. 19 (1984), no. 2, 283 – 297. · Zbl 0547.53034 |
| [2] | S. Brendle and R. Schoen, Manifolds with \( 1/4\)-pinched curvature are space forms, arXiv:math.DG/0705.0766 v2 May 2007. · Zbl 1251.53021 |
| [3] | S. Brendle and R. Schoen, Classification of manifolds with weakly \( 1/4\)-pinched curvatures, arXiv:math.DG/0705.3963 v1 May 2007. · Zbl 1157.53020 |
| [4] | Huai Dong Cao and Bennett Chow, Compact Kähler manifolds with nonnegative curvature operator, Invent. Math. 83 (1986), no. 3, 553 – 556. · Zbl 0604.53026 · doi:10.1007/BF01394422 |
| [5] | Richard S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), no. 2, 153 – 179. · Zbl 0628.53042 |
| [6] | Richard S. Hamilton, The formation of singularities in the Ricci flow, Surveys in differential geometry, Vol. II (Cambridge, MA, 1993) Int. Press, Cambridge, MA, 1995, pp. 7 – 136. · Zbl 0867.53030 |
| [7] | Alan Howard, Brian Smyth, and H. Wu, On compact Kähler manifolds of nonnegative bisectional curvature. I, Acta Math. 147 (1981), no. 1-2, 51 – 56. , https://doi.org/10.1007/BF02392867 H. Wu, On compact Kähler manifolds of nonnegative bisectional curvature. II, Acta Math. 147 (1981), no. 1-2, 57 – 70. · Zbl 0473.53056 · doi:10.1007/BF02392868 |
| [8] | Ngaiming Mok, The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature, J. Differential Geom. 27 (1988), no. 2, 179 – 214. · Zbl 0642.53071 |
| [9] | Shigefumi Mori, Projective manifolds with ample tangent bundles, Ann. of Math. (2) 110 (1979), no. 3, 593 – 606. · Zbl 0423.14006 · doi:10.2307/1971241 |
| [10] | Yum Tong Siu and Shing Tung Yau, Compact Kähler manifolds of positive bisectional curvature, Invent. Math. 59 (1980), no. 2, 189 – 204. · Zbl 0442.53056 · doi:10.1007/BF01390043 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
