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On pseudo-holomorphic curves from two-spheres into a complex Grassmannian G(2, 5)

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Abstract

Let s: S 2 → G(2, 5) be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G(2, 5). It is prove that K is either 1/2 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/2 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or 4/3 if s is a non-degenerate holomorphic curve under some conditions.

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Authors and Affiliations

  1. Department of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing, 100049, P. R. China

    Xiao Xiang Jiao

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  1. Xiao Xiang Jiao
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Correspondence to Xiao Xiang Jiao.

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Supported by National Natural Science Foundation of China (Grant No. 10531090), Knowledge Innovation Funds of CAS (KJCX3-SYW-S03), SRF for ROCS, SEM and the President Fund of GUCAS

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Jiao, X.X. On pseudo-holomorphic curves from two-spheres into a complex Grassmannian G(2, 5). Acta. Math. Sin.-English Ser. 26, 759–762 (2010). https://doi.org/10.1007/s10114-010-7262-0

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  • DOI: https://doi.org/10.1007/s10114-010-7262-0

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