Quantization of curvature of harmonic two-spheres in Grassmann manifolds

Zheng, Yunbo

doi:10.1090/S0002-9947-1989-0935535-6

Quantization of curvature of harmonic two-spheres in Grassmann manifolds
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by Yunbo Zheng

Trans. Amer. Math. Soc. 316 (1989), 193-214

DOI: https://doi.org/10.1090/S0002-9947-1989-0935535-6

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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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Harmonic maps into Grassmann manifolds