Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SEMI-INVARIANT MINIMAL SUBMANIFOLDS OF CONDIMENSION 3 IN A COMPLEX SPACE FORM

  • Published : 2000.10.01
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Abstract

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).

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References

  1. Proc. Amer. Math. Soc. v.69 CR-submanifolds of a Kagerian manifold I A. Bejancu
  2. Geomery of CR-submanifolds A. Bejancu
  3. J. reine angew Math. v.395 Real Hypersurfaces with constant principal curvatures in a hyperbolic space J. Berndt
  4. Kodai Math. Sem. Rep. v.27 Semi-invariant immersion D.E.Blair;G.D. Ludden;K. Yano
  5. Trans. Amer. Math. Soc. v.269 Focal sets and real gypersurfaces in complex projective space T. E. Ceil;P.J. Ryan
  6. Acta. Math. Hungar v.80 Real hypersurfaces of a complex projective space in terms of the Jacobi operator J. Tj. Cho;U-H. Ki
  7. Arch. Math. v.68 Scalar curvature of a certain CR-submanifold of a complex projective space Y.-W. Choe;M. Okumura
  8. J. Differential Geom. v.5 Reduction fo the codimension of and isometric immersion J. Erbacher
  9. Tsukuba J. Math. v.12 Cyclic-parallel real hypersurfaces of a complex projective space U-G. Ki
  10. Tsukuba J. Math. v.13 Real hypersurfaces with parallel Ricci tensor of a complex sapce U-G. Ki
  11. Korean Annals of Math. v.15 A survey on real hypersurfaces in a complex space form U-G. Ki
  12. Kyungpook Math. J. v.40 Semi-invariant submanifolds with lift-flat normal connection in a complex projective space U-G. Ki;H.-J. Kim
  13. J. Korean Math. Soc. v.27 Semi-invariant suvmanifolds wiht garmonic curnature U-H. Ki;S. -J. Kim;S.-B. Lee;I.-Y. Yoo
  14. Nigonkai Math. J. v.11 Suvmanifolds of codimension 3 admitting almost contact metric structure a complex projective space U-H. K;H. Song;R. Takagi
  15. Trans. Amer. Math. Soc. v.296 Real hypersurfaces and complex submanifolds in complex projective space M. kimura
  16. Saitama Math. J. v.15 CR-submanifolds of (n-1) CR-dimension in a complex projective space J. H. Kwon;J. S. Pak
  17. J. Differential Geom. v.4 Rigidity theorems in rank-1 symmetric spaces H. B. Lawson Jr
  18. Proc. Amer. Math. Soc. v.122 Ricci tensors of real hypersurfaces in a complex projective space S. Maeda
  19. J. Math. Soc. Japan v.37 Real hypersurfaces of a complex hyperbolec space S. Montiel
  20. Geom. Dedicata v.20 On some real hypersurfaces of a complex hyperbolec space S. Montiel;A. Romoro
  21. Trans. Amer. Math. Soc. v.212 On some real hypersurfaces in a complex projective space M. Okumura
  22. Geometriae Didicata v.7 Normal curvature and real submanifold of the complex projective space M. Okumura
  23. Collo. Math. Janos Bolyai Dig. Geom. v.56 Codimension reduction problem for real submanifold of complex projectie space M. Okumura
  24. Rendicomti del circolo Mat. di Palermo v.43 n-dimensional real submanifolds with(n-1)dimensional maximal holomorphic tangent subspace in complex projective spaces M. Okumura;l. Vanheke
  25. Osaka J. Math. v.10 On homogeneous real hypersurfaces in a complex projective space R. Takagi
  26. J. Math. Soc. Japan v.27 Real hypersurfaces in a complex projective space with constant principal curvatures Ⅰ,Ⅱ R. Takagi
  27. Sugaku in Japaness v.16 Relations between the theory of almost complex spaces and that of almost comtact space Y. Tashiro
  28. Kodai Math. Sem. Rep. v.29 On (f,g,u,v,w,λ,μ,ν)-structure satisfying λ²+μ²+ν²=1 K. Yano;U-H. Ki
  29. CR submanifolds of Kaehlerian and Sasakian manifolds K. Yano;M. Kon
  30. Structures on manifolds K. Yano;M. Kon