## Tokyo Journal of Mathematics

### Real Hypersurfaces of Complex Quadric in Terms of Star-Ricci Tensor

Xiaomin CHEN

#### 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 $\mathbb{C}P^\frac{m}{2}\subset Q^{m},m\geq4$.

#### Article information

Source
Tokyo J. Math., Volume 41, Number 2 (2018), 587-601.

Dates
First available in Project Euclid: 18 December 2017

https://projecteuclid.org/euclid.tjm/1513566023

Mathematical Reviews number (MathSciNet)
MR3908812

Zentralblatt MATH identifier
07053494

#### Citation

CHEN, Xiaomin. Real Hypersurfaces of Complex Quadric in Terms of Star-Ricci Tensor. Tokyo J. Math. 41 (2018), no. 2, 587--601. https://projecteuclid.org/euclid.tjm/1513566023

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