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REAL HYPERSURFACES IN COMPLEX SPACE FORMS ATTAINING EQUALITY IN AN INEQUALITY INVOLVING A CONTACT δ-INVARIANT

Part of: Global differential geometry Local differential geometry

Published online by Cambridge University Press:  24 September 2020

TORU SASAHARA
TORU SASAHARA*
Affiliation:
Division of Mathematics, Hachinohe Institute of Technology, Hachinohe, Aomori 031-8501, Japan e-mail: sasahara@hi-tech.ac.jp
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Abstract

We investigate real hypersurfaces in nonflat complex space forms attaining equality in an inequality involving the contact δ-invariant δc(2) introduced by Chen and Mihai in [3].

MSC classification

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Secondary: 53B25: Local submanifolds
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 3 , September 2021 , pp. 724 - 731
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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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.CrossRefGoogle Scholar
Chen, B. Y., A general inequality for submanifolds in complex space forms and its applications, Arch. Math. 67 (1996), 519–528.CrossRefGoogle Scholar
Chen, B. Y. and Mihai, I., Isometric immersions of contact Riemannian manifolds in real space forms, Houston J. Math. 31 (2005), 743–764.Google Scholar
Díaz-Ramos, J. C. and Domínguez-Vázquez, M., Non-Hopf real hypersurfaces with constant principal curvatures in complex space forms, Indiana Univ. Math. J. 60 (2011), 859–882.CrossRefGoogle Scholar
Ivey, T. A. and Ryan, P. J., Hypersurfaces in ℂP 2 and ℂH 2 with two distinct principal curvatures, Glasgow Math. J. 58 (2016), 137–152.CrossRefGoogle Scholar
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, Cambridge, 1998), 233–305.Google Scholar
Sasahara, T., Real hypersurfaces in the complex projective plane attaining equality in a basic equality, Houston J. Math. 43 (2017), 89–94.Google Scholar