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Real Hypersurfaces in a Nonflat Complex Space Form with Special Structure Tensor Field

김훈주|임동호
한국수학교육학회|2021.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제28권 제3호|pp. 247-252|DOI https://doi.org/10.7468/jksmeb.2021.28.3.247

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키워드

Hopf hypersurfacereal hypersurfacemodel spacesdifferential operator of structure tensor field
주제분류수학

초록

Let $M$ be a real hypersurface in a complex space form ${M_n(c)}$, $c\neq 0$. In this paper, we prove that if $({\nabla_X}\phi)Y+({\nabla_Y}\phi)X=0$ holds on $M$, then $M$ is a Hopf hypersurface, where $\phi$ is the tangential projection of the complex structure of ${M_n(c)}$. We characterize such Hopf hypersurfaces of ${M_n(c)}.

Abstract

Let $M$ be a real hypersurface in a complex space form ${M_n(c)}$, $c\neq 0$. In this paper, we prove that if $({\nabla_X}\phi)Y+({\nabla_Y}\phi)X=0$ holds on $M$, then $M$ is a Hopf hypersurface, where $\phi$ is the tangential projection of the complex structure of ${M_n(c)}$. We characterize such Hopf hypersurfaces of ${M_n(c)}.

참고문헌 (9)

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  3. 임동호, "Non-existance Real Hypersurfaces in a Nonflat Complex Space Form with Codazzi Type of Structure Tensor Field", 순수 및 응용수학, 28(1), pp.55~60 (2021), 한국수학교육학회[DOI]
  4. D. H. Lim, "Characterizations of real hypersurfaces in a non at complex space form with respect to structure tensor fleld", Far East. J. Math. Scie., 104, pp.277~284 (2018)
  5. S. Maeda, "Real hypersurfaces of a complex projective space in terms of Holomorphic distribution", Tsukuba J. Math, 14, pp.39~52 (1990)
  6. S. Montiel, "On some real hypersurfaces of a complex hyperbolic space", Geometriae Dedicata, 20, pp.245~261 (1986)
  7. R. Niebergall, "Tight and Taut submanifolds", pp.233~305 (1998), Cambridge Univ. Press
  8. M. Okumura, "On some real hypersurfaces of a complex projective space", Trans. Amer. Math. Soc., 212, pp.355~364 (1975)
  9. R. Takagi, "On homogeneous real hypersurfaces in a complex projective space", Osaka J. Math., 10, pp.495~506 (1973)

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