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Proceedings of the American Mathematical Society

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

 

 

Riemann surfaces in complex projective spaces


Authors: Bang-yen Chen and Gerald D. Ludden
Journal: Proc. Amer. Math. Soc. 32 (1972), 561-566
MSC: Primary 53.20; Secondary 30.00
MathSciNet review: 0290262
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Abstract: The complex projective line and the complex quadric are the only compact Riemann surfaces in the complex projective plane with constant scalar normal curvature.


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

  • [1] Bang-yen Chen, Pseudo-umbilical submanifolds of a Riemannian manifold of constant curvature. II, J. Math. Soc. Japan 25 (1973), 105–114. MR 0326622
  • [2] Bang-yen Chen and Gerald D. Ludden, Surfaces with mean curvature vector parallel in the normal bundle, Nagoya Math. J. 47 (1972), 161–167. MR 0331231
  • [3] S. S. Chern, M. do Carmo, and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 59–75. MR 0273546
  • [4] Takehiro Itoh, Minimal surfaces in 4-dimensional Riemannian manifolds of constant curvature, Kōdai Math. Sem. Rep. 24 (1972), 451–458. MR 0317248

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0290262-9
Keywords: Complex projective space, complex quadric, scalar normal curvature, Kähler manifold, second fundamental form
Article copyright: © Copyright 1972 American Mathematical Society