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Generating Curves of Minimal Ruled Real Hypersurfaces in a Nonflat Complex Space Form

  • Sadahiro Maeda (a1), Hiromasa Tanabe (a2) and Seiichi Udagawa (a3)
Abstract

We first provide a necessary and sufficient condition for a ruled real hypersurface in a nonflat complex space form to have constant mean curvature in terms of integral curves of the characteristic vector field on it. This yields a characterization of minimal ruled real hypersurfaces by circles. We next characterize the homogeneous minimal ruled real hypersurface in a complex hyperbolic space by using the notion of strong congruency of curves.

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[1] Adachi, T., Bao, T., and Maeda, S., Congruence classes of minimal ruled real hypersurfaces in a nonflat complex space form . Hokkaido Math. J. 43(2014), 137150. https://doi.org/10.14492/hokmj/1392906097.
[2] Adachi, T. and Maeda, S., Global behaviours of circles in a complex hyperbolic space . Tsukuba J. Math. 21(1997), 2942. https://doi.org/10.21099/tkbjm/1496163159.
[3] Adachi, T., Maeda, S., and Udagawa, S., Circles in a complex projective space . Osaka J. Math. 32(1995), 709719.
[4] Berndt, J. and Tamaru, H., Cohomogeneity one actions on noncompact symmetric spaces of rank one . Trans. Amer. Math. Soc. 359(2007), 34253438. https://doi.org/10.1090/S0002-9947-07-04305-X.
[5] Domínguez-Vázquez, M. and Pérez-Barral, O., Ruled hypersurfaces with constant mean curvature in complex space forms. arxiv:1802.09341.
[6] Lohnherr, M. and Reckziegel, H., On ruled real hypersurfaces in complex space forms . Geom. Dedicata 79(1999), 267286. https://doi.org/10.1023/A:1005000122427.
[7] Maeda, S. and Ohnita, Y., Helical geodesic immersions into complex space forms . Geom. Dedicata 30(1989), 93114. https://doi.org/10.1007/BF02424315.
[8] Niebergall, R. and Ryan, P. J., Real hypersurfaces in complex space forms . In: Tight and taut submanifolds, Cambridge University Press, Cambridge, 1998, pp. 233305.
[9] Takagi, R., On homogeneous real hypersurfaces in a complex projective space . Osaka J. Math. 10(1973), 495506.
[10] Takagi, R., Real hypersurfaces in a complex projective space with constant principal curvatures. II . J. Math. Soc. Japan 27(1975), 507516. https://doi.org/10.2969/jmsj/02740507.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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