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The homogeneous ruled real hypersurface in a complex hyperbolic space

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Abstract

We characterize the homogeneous ruled real hyperurface of a complex hyperbolic space in the class of ruled real hypersurfaces having constant mean curvature.

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References

  1. Adachi, T., Bao, T., Maeda, S.: Congruence classes of minimal ruled real hypersurfaces in a nonflat complex space form. Hokkaido Math. J. 43, 1–14 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Berndt, J., Tamaru, H.: Cohomogeneity one actions on noncompact symmetric spaces of rank one. Trans. Am. Math. Soc. 359, 3425–3438 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kimura, M.: Sectional curvatures of holomorphic planes on a real hypersurface in \(\,P^{n}(C)\). Math. Ann. 276, 487–497 (1987)

  4. Lohnherr, M., Reckziegel, H.: On ruled real hypersurfaces in complex space forms. Geom. Dedicata 79, 267–286 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Maeda, S., Tanabe, H.: A characterization of the homogeneous ruled real hypersurface in a complex hyperbolic space in terms of the first curvature of some integral curves. Arch. Math. (Basel) 105, 593–599 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Maeda, S., Tamaru, H., Tanabe, H.: Curvature properties of homogeneous real hypersurfaces in nonflat complex space forms. To appear in Kodai Math. J.

  7. Takagi, R.: On homogeneous real hypersurfaces in a complex projective space. Osaka J. Math. 10, 495–506 (1973)

    MathSciNet  MATH  Google Scholar 

  8. Takagi, R.: Real hypersurfaces in a complex projective space with constant principal curvatures \(\,{\rm II}\). J. Math. Soc. Jpn. 27, 507–516 (1975)

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Correspondence to Hiromasa Tanabe.

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Makoto Kimura is supported by JSPS KAKENHI Grant Number JP16K05119.

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Kimura, M., Maeda, S. & Tanabe, H. The homogeneous ruled real hypersurface in a complex hyperbolic space. J. Geom. 109, 16 (2018). https://doi.org/10.1007/s00022-018-0421-7

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  • DOI: https://doi.org/10.1007/s00022-018-0421-7

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