Real hypersurfaces with Reeb invariant shape operator in the complex hyperbolic quadric

Doo Hyun Hwang                <meta name=

2023/102/3-4 (4) — DOI: 10.5486/PMD.2023.9391 — pp. 323-342

Real hypersurfaces with Reeb invariant shape operator in the complex hyperbolic quadric

Authors: Doo Hyun Hwang, Juan de Dios Pérez and Young Jin Suh

Abstract:

First, we introduce the notion of Reeb invariant shape operator for real hypersurfaces in the complex hyperbolic quadric ${{Q^m}^*} = SO^{o}_{2,m}/SO_mSO_2$, $m \geq 3$. Next, we give a complete classification of real hypersurfaces with Reeb invariant shape operator in the complex hyperbolic quadrics ${{Q^m}^*}$.

Keywords: Reeb invariant, real hypersurface, isometric Reeb flow, $\mathfrak A$-isotropic singular, complex hyperbolic quadric

Mathematics Subject Classification: 53C40, 53C55