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

Part of: Global differential geometry Local differential geometry

Published online by Cambridge University Press:  09 January 2019

Sadahiro Maeda ,
Hiromasa Tanabe  and
Seiichi Udagawa
Sadahiro Maeda
Affiliation:
Department of Mathematics, Saga University, 1 Honzyo, Saga 840-8502, Japan Email: [email protected]
Hiromasa Tanabe
Affiliation:
Department of Science, National Institute of Technology, Matsue College, Matsue, Shimane 690-8518, Japan Email: [email protected]
Seiichi Udagawa
Affiliation:
Department of Mathematics, School of Medicine, Nihon University, Itabashi, Tokyo 173-0032, Japan Email: [email protected]
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Abstract

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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.

Keywords

nonflat complex space formminimal ruled real hypersurfaceconstant mean curvatureintegral curves of the characteristic vector field

MSC classification

Primary: 53B25: Local submanifolds
Secondary: 53C40: Global submanifolds
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 2 , June 2019 , pp. 383 - 392
Copyright
© Canadian Mathematical Society 2018 

References

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), 137–150. https://doi.org/10.14492/hokmj/1392906097.Google Scholar
Adachi, T. and Maeda, S., Global behaviours of circles in a complex hyperbolic space . Tsukuba J. Math. 21(1997), 29–42. https://doi.org/10.21099/tkbjm/1496163159.Google Scholar
Adachi, T., Maeda, S., and Udagawa, S., Circles in a complex projective space . Osaka J. Math. 32(1995), 709–719.Google Scholar
Berndt, J. and Tamaru, H., Cohomogeneity one actions on noncompact symmetric spaces of rank one . Trans. Amer. Math. Soc. 359(2007), 3425–3438. https://doi.org/10.1090/S0002-9947-07-04305-X.Google Scholar
Domínguez-Vázquez, M. and Pérez-Barral, O., Ruled hypersurfaces with constant mean curvature in complex space forms. arxiv:1802.09341.Google Scholar
Lohnherr, M. and Reckziegel, H., On ruled real hypersurfaces in complex space forms . Geom. Dedicata 79(1999), 267–286. https://doi.org/10.1023/A:1005000122427.Google Scholar
Maeda, S. and Ohnita, Y., Helical geodesic immersions into complex space forms . Geom. Dedicata 30(1989), 93–114. https://doi.org/10.1007/BF02424315.Google Scholar
Niebergall, R. and Ryan, P. J., Real hypersurfaces in complex space forms . In: Tight and taut submanifolds, Cambridge University Press, Cambridge, 1998, pp. 233–305.Google Scholar
Takagi, R., On homogeneous real hypersurfaces in a complex projective space . Osaka J. Math. 10(1973), 495–506.Google Scholar
Takagi, R., Real hypersurfaces in a complex projective space with constant principal curvatures. II . J. Math. Soc. Japan 27(1975), 507–516. https://doi.org/10.2969/jmsj/02740507.Google Scholar