Riemann surfaces in complex projective spaces
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- by Bang-yen Chen and Gerald D. Ludden PDF
- Proc. Amer. Math. Soc. 32 (1972), 561-566 Request permission
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
- Bang-yen Chen, Pseudo-umbilical submanifolds of a Riemannian manifold of constant curvature. II, J. Math. Soc. Japan 25 (1973), 105–114. MR 326622, DOI 10.2969/jmsj/02510105
- 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 331231
- 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
- Takehiro Itoh, Minimal surfaces in $4$-dimensional Riemannian manifolds of constant curvature, K\B{o}dai Math. Sem. Rep. 24 (1972), 451–458. MR 317248
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 561-566
- MSC: Primary 53.20; Secondary 30.00
- DOI: https://doi.org/10.1090/S0002-9939-1972-0290262-9
- MathSciNet review: 0290262