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SHAPE OPERATOR AH FOR SLANT SUBMANIFOLDS IN GENERALIZED COMPLEX SPACE FORMS

KIM, DONG-SOO    (Department of Mathematics, Chonnam National University   ); KIM, YOUNG-HO    (Department of Mathematics, Kyungpook National University   ); LEE, CHUL-WOO    (Department of Mathematics, Kyungpook National University  );
  • 초록

    In this article, we establish relations between the sectional curvature function K and the shape operator, and also relationship between the k-Ricci curvature and the shape operator for slant submanifolds in generalized complex space forms with arbitrary codimension.


  • 주제어

    shape operator .   scalar curvature .   squared mean curvature .   k-Ricci curvature .   generalized complex space form .   complex space form .   real space form .   slant submanifold .   invariant and anti-invariant submanifild.  

  • 참고문헌 (13)

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    3. B.-Y. Chen, Mean curvature and shape operator of isometric immersions in real space form, Glasg. Math. J. 38 (1996), 87-97 
    4. B.-Y. Chen, Relations betveen Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasg. Math. J. 41 (1999), 33-41 
    5. A. Gray, Nearly Kaehler manifolds, J. Differential Geom. 4 (1970), 283-309 
    6. J. J. Konderak, An example of an almost Hermitian fiat manifold which is not Hermitian, Riv. Mat. Univ. Parma (4), 17 (1991), 3159-318 
    7. K. Matsumoto, I. Mihai, and A. Oiaga, Shape operator for slant sub manifold in complex space forms, Bull. Yamagata Univ. Natur. Sci. 14 (2000), 169-177 
    8. Z. Olszak, On the existence of generalized complex space forms, Israel J. Math. 65 (1989), 214-218 
    9. G.-B. Rizza, Varieta parakahleruuie, Ann. Mat. Pura Appl. 98 (1974), 47-61 
    10. F. Triccrri, Flat almost Hermitian manifolds which are not Kahler manifolds, Tensor (N.S.) 13 (1977), 149-154 
    11. M. M. Tripathi, Some remarks on almost Hermitian Manifolds, Riv. Mat. Univ. Parma 3 (1994), no. 5, 229-230 
    12. L. Vanhecke, Almost Hermitian manifolds with J-invariant Riemann curvature tensor, Rend. Mat. 34 (1975/76), 487-498 
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    2. 1993 "A CHARACTERIZATION OF TOTALLY UMBILIC SUBMANIFOLDS" Communications of the Korean Mathematical Society = 대한수학회논문집 8 (3): 483~488    
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    4. 1994 "SPACE CURVES SATISFYING $\Delta$H = AH" Bulletin of the Korean Mathematical Society = 대한수학회보 31 (2): 193~200    
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  • LEE, CHUL WOO (52)

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