A new classification on parallel Ricci tensor for real hypersurfaces in the complex quadric. Issue 6 (December 2021)

• Record Type: Journal Article
• Authors: Lee, Hyunjin; Suh, Young Jin
• Is Part Of: Proceedings. Volume 151:Issue 6(2021)
• Page Start: 1846
• Page End: 1868
• Publication Date: 2021-12
• Subjects: Parallel Ricci tensor -- $\mathfrak {A}$-isotropic -- $\mathfrak {A}$-principal -- Kähler structure -- complex conjugation -- complex quadric; 53C40 -- 53C55; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2020.83
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : First we introduce the notion of parallel Ricci tensor ${\nabla }\mathrm {Ric}=0$ for real hypersurfaces in the complex quadric Q m = SO m +2 / SO m SO 2 and show that the unit normal vector field N is singular. Next we give a new classification of real hypersurfaces in the complex quadric Q m = SO m +2 / SO m SO 2 with parallel Ricci tensor.