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Non-existence of conformally flat real hypersurfaces in both the complex quadric and the complex hyperbolic quadric

Part of: Global differential geometry Local differential geometry

Published online by Cambridge University Press:  15 February 2021

Zeke Yao ,
Bangchao Yin  and
Zejun Hu
Zeke Yao
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou450001, P.R. China e-mail: yaozkleon@163.commathyinchao@163.com
Bangchao Yin
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou450001, P.R. China e-mail: yaozkleon@163.commathyinchao@163.com
Zejun Hu*
Affiliation:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou450001, P.R. China e-mail: yaozkleon@163.commathyinchao@163.com
*
Zejun Hu is the corresponding author. e-mail: huzj@zzu.edu.cn
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Abstract

In this paper, by applying for a new approach of the so-called Tsinghua principle, we prove the nonexistence of locally conformally flat real hypersurfaces in both the m-dimensional complex quadric $Q^m$ and the complex hyperbolic quadric $Q^{m\ast }$ for $m\ge 3$ .

Keywords

Complex quadriccomplex hyperbolic quadricconformally flat hypersurfacereal hypersurface𝔄-principalTsinghua principle

MSC classification

Primary: 53B25: Local submanifolds
Secondary: 53C40: Global submanifolds 53C55: Hermitian and Kählerian manifolds
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 1 , March 2022 , pp. 68 - 83
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

This project was supported by NSF of China, Grant Number 11771404.

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