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Some totally real minimal surfaces in $ CP\sp{2}$


Author: Chorng-shi Houh
Journal: Proc. Amer. Math. Soc. 40 (1973), 240-244
MSC: Primary 53A10; Secondary 53C45
DOI: https://doi.org/10.1090/S0002-9939-1973-0317189-9
MathSciNet review: 0317189
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Abstract: Totally real minimal surfaces with constant scalar normal curvature in $ C{P^2}$ are totally geodesic or nonpositive curved surfaces.


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

  • [1] B.-Y. Chen and G. D. Ludden, Riemann surfaces in complex projective spaces, Proc. Amer. Math. Soc. 32 (1972), 561-566. MR 44 #7446. MR 0290262 (44:7446)
  • [2] 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 42 #8424. MR 0273546 (42:8424)
  • [3] S. T. Yau, Submanifolds with constant mean curvature. I (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0317189-9
Keywords: Totally real, minimal surface, scalar normal curvature, second fundamental form, totally geodesic
Article copyright: © Copyright 1973 American Mathematical Society

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