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REAL HYPERSURFACES WITH φ-INVARIANT SHAPE OPERATOR IN A COMPLEX PROJECTIVE SPACE

Published online by Cambridge University Press:  08 December 2010

SADAHIRO MAEDA  and
HIROO NAITOH
SADAHIRO MAEDA
Affiliation:
Department of Mathematics, Saga University 1 Honzyo, Saga 840-8502, Japan e-mail: smaeda@ms.saga-u.ac.jp
HIROO NAITOH
Affiliation:
Department of Mathematics, Yamaguchi University Yoshida, Yamaguchi 753-8512, Japan e-mail: naitoh@yamaguchi-u.ac.jp
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Abstract

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We characterize real hypersurfaces of type (A) and ruled real hypersurfaces in a complex projective space in terms of two φ-invariances of their shape operators, and give geometric meanings of these real hypersurfaces by observing their some geodesics.

Keywords

Primary 53B25Secondary 53C4053C22
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 2 , May 2011 , pp. 347 - 358
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Adachi, T. and Maeda, S., A congruence theorem of geodesics on some naturally reductive Riemannian homogeneous manifolds, C. R. Math. Rep. Acad. Sci. Canada 26 (2004), 11–17.Google Scholar
2.Adachi, T., Maeda, S. and Yamagishi, M., Length spectrum of geodesic spheres in a non-flat complex space form, J. Math. Soc. Japan 54 (2002), 373–408.CrossRefGoogle Scholar
3.Ferus, D., Symmetric submanifolds of Euclidean space, Math. Ann. 247 (1980), 81–93.CrossRefGoogle Scholar
4.Kimura, M., Sectional curvatures of holomorphic planes on a real hypersurface in Pn(ℂ), Math. Ann. 276 (1987), 487–497.CrossRefGoogle Scholar
5.Kimura, M. and Maeda, S., On real hypersurfaces of a complex projective space, Math. Z. 202 (1989), 299–311.CrossRefGoogle Scholar
6.Kobayashi, S. and Nagano, T., On filtered Lie algebras and geometric structures I, J. Math. Mech. 13 (1964), 875–907.Google Scholar
7.Maeda, S. and Adachi, T., Integral curves of characteristic vector fields of real hypersurfaces in nonflat complex space forms, Geom. Dedicata 123 (2006), 65–72.CrossRefGoogle Scholar
8.Maeda, S. and Adachi, T., Extrinsic geodesics and hypersurfaces of type (A) in a complex projective space, Tohoku Math. J. 60 (2008), 597–605.Google Scholar
9.Naitoh, H., Grassmann geometries on compact symmetric spaces of general type, J. Math. Soc. Japan 50 (3) (1998), 557–592.CrossRefGoogle Scholar
10.Niebergall, R. and Ryan, P. J., Real hypersurfaces in complex space forms, in: Tight and Taut submanifolds (Cecil, T. E. and Chern, S. S., Editors) (Cambridge University Press, 1998), 233–305.Google Scholar
11.Naitoh, H. and Takeuchi, M., Symmetric submanifolds of symmetric spaces, Sugaku Expositions 2 (2) (1989), 157–188.Google Scholar