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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Minimal surfaces with constant Kähler angle in complex projective spaces


Author: Xiao Huan Mo
Journal: Proc. Amer. Math. Soc. 121 (1994), 569-571
MSC: Primary 53C42
DOI: https://doi.org/10.1090/S0002-9939-1994-1185271-6
MathSciNet review: 1185271
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Abstract: Let $ \psi :{S^2} \to C{P^n}$ be an isometric minimal immersion of the Riemann sphere $ {S^2}$ into $ C{P^n}$ with constant Kähler angle $ \theta $. In this paper, we prove that Bolton et al.'s conjecture holds if $ \theta $ is not too close to $ \frac{\pi }{2}$, that is, $ \psi $ is $ \pm $ holomorphic or belongs to the Veronese sequence if $ \vert\cos \theta \vert \geq \frac{1}{5}$.


References [Enhancements On Off] (What's this?)

  • [1] John Bolton, Gary R. Jensen, Marco Rigoli, and Lyndon M. Woodward, On conformal minimal immersions of $ {S^2}$ into $ C{P^n}$, Math. Ann. 279 (1988), 599-620. MR 926423 (88m:53110)
  • [2] S. S. Chern and J. G. Wolfson, Minimal surfaces by moving frame, Amer. J. Math. 105 (1983), 59-83. MR 692106 (84i:53056)
  • [3] S. Bando and Y. Ohnita, Minimal 2-spheres with constant curvature in $ {P_n}(C)$, J. Math. Soc. Japan 39 (1987), 477-487. MR 900981 (88i:53097)

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DOI: https://doi.org/10.1090/S0002-9939-1994-1185271-6
Article copyright: © Copyright 1994 American Mathematical Society

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