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
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