Derivatives of normal Jacobi operator on real hypersurfaces in the complex quadric. Issue 6 (25th June 2020)

• Record Type: Journal Article
• Authors: Lee, Hyunjin; Pérez, Juan de Dios; Suh, Young Jin
• Is Part Of: Bulletin of the London Mathematical Society. Volume 52:Issue 6(2020)
• Page Start: 1122
• Page End: 1133
• Publication Date: 2020-06-25
• Subjects: 53C40 (primary) -- 53C55 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12386
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: Suh ( Math. Nachr . 290 (2017) 442–451) proved that there are no Hopf real hypersurfaces in the complex quadric that have parallel normal Jacobi operators. Motivated by this result, in this paper, we introduce the notions of C ‐parallel and Reeb parallel for normal Jacobi operators, which generalize the notion 'parallel'. First we obtain a non‐existence theorem of Hopf real hypersurfaces with C ‐parallel normal Jacobi operator in the complex quadric Q m for m ⩾ 3 . We then prove that a Hopf real hypersurface has a Reeb parallel normal Jacobi operator if and only if it has an A ‐isotropic singular normal vector field.