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Positively curved totally real minimal submanifolds immersed in a complex projective space


Author: Koichi Ogiue
Journal: Proc. Amer. Math. Soc. 56 (1976), 264-266
DOI: https://doi.org/10.1090/S0002-9939-1976-0400129-4
MathSciNet review: 0400129
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Abstract | References | Additional Information

Abstract: A sufficient condition for a complete totally real minimal submanifold immersed in a complex projective space to be totally geodesic is given in terms of sectional curvature.


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

  • [1] B. Y. Chen and K. Ogiue, On totally real submanifolds, Trans. Amer. Math. Soc. 193(1974), 257-266. MR 0346708 (49:11433)
  • [2] S. S. Chern, M. P. 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. of 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, Amer. J. Math. 96(1974), 346-366. MR 0370443 (51:6670)
  • [4] -, Submanifolds with constant mean curvature. II, Amer. J. Math. 97 (1975), 76-100.


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0400129-4
Keywords: Totally real submanifold, minimal submanifold, complex projective space, totally geodesic
Article copyright: © Copyright 1976 American Mathematical Society

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