Derivatives of normal Jacobi operator on real hypersurfaces in the complex quadric

2020/05/06 by Hyunjin Lee, Juan de Dios Pérez, Young Jin Suh
Mathematics · #math.DG #msc:53C40 #msc:53C55

paper · pdf · doi:10.1112/blms.12386

12 pages. arXiv admin note: substantial text overlap with arXiv:1907.04661, arXiv:2003.07231, arXiv:1512.03671, arXiv:1605.05316

arxiv created 2020/05/06 · arxiv updated 2020/07/08

Abstract

In \citeS 2017, Suh gave a non-existence theorem for Hopf real hypersurfaces in the complex quadric with parallel normal Jacobi operator. Motivated by this result, in this paper, we introduce some generalized conditions named \mathcal C-parallel or Reeb parallel normal Jacobi operators. By using such weaker parallelisms of normal Jacobi operator, first we can assert a non-existence theorem of Hopf real hypersurfaces with \mathcal C-parallel normal Jacobi operator in the complex quadric Q^m, m ≥ 3. Next, we prove that a Hopf real hypersurface has Reeb parallel normal Jacobi operator if and only if it has an \mathfrak A-isotropic singular normal vector field.

Citations

• Real hypersurfaces in the complex quadric with Reeb parallel structure Jacobi operator
• Real hypersurfaces in the complex quadric with commuting Ricci tensor
• Real hypersurfaces in the complex quadric with parallel structure Jacobi operator