Parallel real hypersurfaces in $\mathbb{S}^2\times\mathbb{S}^2$ and $\mathbb{H}^2\times\mathbb{H}^2$ with respect to the $k$-generalized Tanaka--Webster connection
Abstract
In this paper, we first characterize real hypersurfaces of both the K\"ahler surfaces $\mathbb{S}^2\times\mathbb{S}^2$ and $\mathbb{H}^2\times\mathbb{H}^2$ such that their shape operators have identical covariant derivatives with respect to the Levi-Civita connection and the $k$-generalized Tanaka--Webster connection for a nonzero $k\in\mathbb{R}$. Then, amongst others, we classify all real hypersurfaces of both $\mathbb{S}^2\times\mathbb{S}^2$ and $\mathbb{H}^2\times\mathbb{H}^2$ whose shape operators are parallel with respect to the $k$-generalized Tanaka--Webster connection.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Publicationes Mathematicae Debrecen
- Volume
- 108
- Issue
- 1-2
- Pages
- 25–44
- Publication date
- 1 January 2026