Hostname: page-component-7c8c6479df-ws8qp Total loading time: 0 Render date: 2024-03-29T04:44:55.334Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  24 September 2020

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

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].

Type
Research Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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), 137150.CrossRefGoogle Scholar
Chen, B. Y., A general inequality for submanifolds in complex space forms and its applications, Arch. Math. 67 (1996), 519528.CrossRefGoogle Scholar
Chen, B. Y. and Mihai, I., Isometric immersions of contact Riemannian manifolds in real space forms, Houston J. Math. 31 (2005), 743764.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), 859882.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), 137152.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), 8994.Google Scholar