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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Quantization of curvature of harmonic two-spheres in Grassmann manifolds


Author: Yunbo Zheng
Journal: Trans. Amer. Math. Soc. 316 (1989), 193-214
MSC: Primary 58E20; Secondary 53C42
MathSciNet review: 935535
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Abstract: Various pinching theorems for curvature of minimal two-spheres in Grassmann manifolds have been proved. In particular, we show that when the curvature is large, then the minimal map from $ {S^2}$ into $ G(m,N)$ must be either holomorphic or antiholomorphic. Also, minimal two-spheres of curvature $ \kappa \geqslant 2$ in $ G(2,4)$ have been classified.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0935535-6
PII: S 0002-9947(1989)0935535-6
Keywords: Harmonic maps, pseudoholomorphic, pinching
Article copyright: © Copyright 1989 American Mathematical Society