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December 2018 Real Hypersurfaces of Complex Quadric in Terms of Star-Ricci Tensor
Xiaomin CHEN
Tokyo J. Math. 41(2): 587-601 (December 2018). DOI: 10.3836/tjm/1502179254

Abstract

In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric $Q^m$. It is proved that there exist no Hopf hypersurfaces in $Q^m,m\geq3$, with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on $M$ are considered. In this case we show that $M$ is an open part of a tube around a totally geodesic $\mathbb{C}P^\frac{m}{2}\subset Q^{m},m\geq4$.

Citation

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Xiaomin CHEN. "Real Hypersurfaces of Complex Quadric in Terms of Star-Ricci Tensor." Tokyo J. Math. 41 (2) 587 - 601, December 2018. https://doi.org/10.3836/tjm/1502179254

Information

Published: December 2018
First available in Project Euclid: 18 December 2017

zbMATH: 07053494
MathSciNet: MR3908812
Digital Object Identifier: 10.3836/tjm/1502179254

Subjects:
Primary: 53C40
Secondary: 53C15

Rights: Copyright © 2018 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
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Vol.41 • No. 2 • December 2018
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