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Bulletin of the Korean Mathematical Society = 대한수학회보 v.42 no.2, 2005년, pp.337 - 358   피인용횟수: 1

THE STRUCTURE JACOBI OPERATOR ON REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM

KI, U-HANG   (DEPARTMENT OF MATHEMATICS, KYUNGPOOK NATIONAL UNIVERSITYUU0000096  ); KIM, SOO-JIN   (DEPARTMENT OF MATHEMATICS, CHOSUN UNIVERSITYUU0001180  ); LEE, SEONG-BAEK   (DEPARTMENT OF MATHEMATICS, CHOSUN UNIVERSITYUU0001180  );
  • 초록

    Let M be a real hypersurface with almost contact metric structure $(\phi,\;\xi,\;\eta,\;g)$ in a nonflat complex space form $M_n(c)$ . In this paper, we prove that if the structure Jacobi operator $R_\xi$ commutes with both the structure tensor $\phi$ and the Ricc tensor S, then M is a Hopf hypersurface in $M_n(c)$ provided that the mean curvature of M is constant or $g(S\xi,\;\xi)$ is constant.


  • 주제어

    structure Jacobi operator .   Ricci tensor .   Hopf hypersurface .   nonflat complex space form.  

  • 참고문헌 (19)

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  • 이 논문을 인용한 문헌 (1)

    1. 2010. "" Honam mathematical journal = 호남수학학술지, 32(4): 747~761     

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  • Ki, U-Hang (24)

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    2. 1982 "GENERIC SUBMANIFOLDS WITH PARALLEL RICCI CURVATURE OF S2m+1(1)" Journal of the Korean Mathematical Society = 대한수학회지 19 (1): 55~60    
    3. 1984 "NEARLY KAEHLERIAN PRODUCT MANIFOLDS OF TWO ALMOST CONTACT METRIC MANIFOLDS" Bulletin of the Korean Mathematical Society = 대한수학회보 21 (2): 61~66    
    4. 1989 "REAL HYPERSURFACES WITH η-HARMONIC WEYL TENSOR OF A COMPLEX SPACE FORM" Journal of the Korean Mathematical Society = 대한수학회지 26 (2): 311~322    
    5. 1991 "SOME CHARACTERIZATIONS OF A REAL HYPERSURFACE OF TYPE A" Kyungpook mathematical journal 31 (1): 73~82    
    6. 1992 "기하학의 발전과 장래" 한국수학사학회지 = The Korean journal for history of mathematics 7 (1): 21~30    
    7. 1994 "COMPLETE MAXIMAL SPACE-LIKE HYPERSURFACES IN AN ANTI-DE SITTER SPACE" Bulletin of the Korean Mathematical Society = 대한수학회보 31 (1): 85~92    
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    9. 1995 "Totally real submanifolds with parallel mean curvature vector in a complex space form" Journal of the Korean Mathematical Society = 대한수학회지 32 (4): 835~848    
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  • Kim, Soo-Jin (2)

  • Lee, Seong-Baek (19)

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