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Proceedings of the American Mathematical Society

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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] B.-Y. Chen, Pseudo-umbilical submanifolds of a Riemannian manifold of constant curvature. III, J. Differential Geometry (to appear). MR 0326622 (48:4965)
  • [2] B.-Y. Chen and G. D. Ludden, Surfaces with mean curvature vector parallel in the normal bundle (to appear). MR 0331231 (48:9565)
  • [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, 1970, pp. 57-75. MR 0273546 (42:8424)
  • [4] T. Itoh, Minimal surfaces in 4-dimensional Riemannian manifold of constant curvature, Kōdai Math. Sem. Rep. (to appear). MR 0317248 (47:5795)

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Keywords: Complex projective space, complex quadric, scalar normal curvature, Kähler manifold, second fundamental form
Article copyright: © Copyright 1972 American Mathematical Society

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