Real hypersurfaces in the complex hyperbolic quadric with parallel structure Jacobi operator

Young Jin Suh; Juan de Dios Pérez; Changhwa Woo

2019/94/1-2 (6) — DOI: 10.5486/PMD.2019.8262 — pp. 75-107

Real hypersurfaces in the complex hyperbolic quadric with parallel structure Jacobi operator

Authors: Young Jin Suh, Juan de Dios Pérez and Changhwa Woo

Abstract:

We introduce the notion of parallel structure Jacobi operator for real hypersurfaces in the complex hyperbolic quadric ${{Q^m}^{\ast}=SO^0_{2,m}/SO_2 SO_m}$, $m\geq 3$, and prove a non-existence result for real hypersurfaces in ${{Q^m}^{\ast}=SO^0_{2,m}/SO_2SO_m}$, $m\geq 3$, with parallel structure Jacobi operator.

Keywords: complex hyperbolic quadric, parallel structure Jacobi operator, $\mathfrak{A}$-isotropic, $\mathfrak{A}$-principal, Kähler structure, complex conjugation

Mathematics Subject Classification: 53C40, 53C55, 53C15