Real hypersurfaces of complex quadric in terms of star-Ricci tensor

2017/10/29 by Xiaomin Chen, Chen, Xiaomin
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1710.10627

openalex publication_date 2017/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥3, 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 ℂP^(m)/(2)⊂ Q^m,m≥4.

Related

• Real hypersurfaces with *-η-Ricci-Yamabe solitons in the complex quadric
• The *-Ricci tensor for hypersurfaces in CPⁿ and CHⁿ
• Gradient pseudo-Ricci solitons of real hypersurfaces
• Real hypersurfaces in Q^m with commuting structure Jacobi operator
• Ricci solitons in manifolds with quasi-constant curvature