Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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J-INVARIANT SUBMANIFOLDS OF CODIMENSION 2 IN A COMPLEX PROJECTIVE SPACE

  • Choe, Yeong-Wu (DEPARTMENT OF MATHEMATICS, CATHOLIC UNIVERSITY OF DAEGU)
  • Published : 2002.05.01
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Abstract

In this paper we prove that if M is a J-invariant sub-manifold of codimension 2 in a complex projective space $P_{n+1}(C)$, and the second fundamental tensor is cyclic-parallel or M has harmonic curvature, then M is locally complex quadric Q$_n$(C) or P$_n$(C).

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References

  1. Y.-W. Choe and M. Okumura, Scalar curvature of a CR-submanifold of complex projective space, Arch. Math. 68 (1997), 340-346. https://doi.org/10.1007/s000130050065
  2. A. Derzirski, Classification of certain compact Riemannian manifolds with harmonic curvature and non-parallel Ricci tensor, Math. z. 172 (1980), 273-280. https://doi.org/10.1007/BF01215090
  3. U-H. Ki, On certain submanifolds of codimension 2 of a locally fubinian manifold, Kodai Math. Sem. Rep. 24 (1972), 17-27. https://doi.org/10.2996/kmj/1138846470
  4. U-H. Ki, Cyclic-parallel real hypersurfaces of a complex space form, Tsukuba J. Math. 12-1 (1988), 259-268.
  5. U-H. Ki and H. Nakagawa, Submanifolds with harmonic curvature, Tsukuba J. Math. 12-1 (1986), 285-292.
  6. S. Kobayashi and K. Nomizu, Foundations of differential geometry I, New York, 1963.
  7. K. Ogiue, Notes in Differential Geometry, Universidad de Granada, Lecture Notes by O. J. Garay, 1985.
  8. M. Okumura, Real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc. 213 (1975), 355-364.
  9. W.-H. Sohn, Some curvature conditions of n-dimensional CR-submanifolds of(n- 1) CR-dimension in a complex projective sapce II, Comm. Korean Math. Soc. 16 (2001), 265-275.
  10. R. Takagi, Real hypersurfaces in a complex projective space, J. Math. Soc. Japan 27 (1975), 506-516. https://doi.org/10.2969/jmsj/02740507
  11. T. Takahashi, Sasakian manifolds with pseudo-Riemannian metric, Tohoku Math. J. 21 (1969), 271-290. https://doi.org/10.2748/tmj/1178242996
  12. K. Yano and M. Kon, CR submanifolds of Kaehlerian and Sasakian manifolds, Birkhäuser, 1983.