Abstract
Let s : S 2 → G(2, n) be a linearly full totally unramified non-degenerate holomorphic curve in a complex Grassmann manifold G(2, n), and let K(s) be its Gaussian curvature. It is proved that \({K(s) = \frac{4}{n-2}}\) if K(s) satisfies \({K(s) \geq \frac{4}{n-2}}\) or \({K(s) \leq \frac{4}{n-2} }\) everywhere on S 2. In particular, \({K(s) = \frac{4}{n-2}}\) if K(s) is constant.
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This work is supported by the National Natural Science Foundation of China (Grant No. 11071248) and Knowledge Innovation Funds of CAS (Grant No. KJCX3-SYW-S03).
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Jiao, X., Yu, Y. On holomorphic curves in a complex Grassmann manifold G(2, n). Arch. Math. 96, 291–300 (2011). https://doi.org/10.1007/s00013-011-0231-8
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DOI: https://doi.org/10.1007/s00013-011-0231-8