Ruled Real Hypersurfaces in the Complex Quadric
Copyright policy )Ruled Real Hypersurfaces in the Complex Quadric
First we introduce the notions of $\eta$-parallel and $\eta$-commuting shape operator for real hypersurfaces in the complex quadric $Q^m = SO_{m+2}/SO_m SO_2$. Next we give a complete classification of real hypersurfaces in the complex quadric $Q^m$ with such king of shape operators. By virtue of this classification we give a new characterization of ruled real hypersurfaces foliated by complex totally geodesic hyperplanes $Q^{m-1}$ in $Q^m$ whose unit normal vector field in $Q^m$ is $\mathfrak{A}$-principal.
MCT-FEDER project MTM-2016-78807-C2-1-P
JSPS KAKENHI Grant Number JP20K03575
NRF-2019-R1I1A1A-01050300
NRF-2018-R1D1A1B-05040381
- UPRRP College of Natural Sciences Puerto Rico
- University of Granada Spain
- Kyungpook National University Korea (Republic of)
- Ibaraki University Japan
ruled real hypersurface, $\mathfrak{A}$-isotropic, Global submanifolds, Complex conjugation, Global differential geometry of Hermitian and Kählerian manifolds, Complex quadric, $\eta$-Parallel shape operator, $\mathfrak{A}$-principal, Ruled real hypersurface, complex conjugation, \(\mathfrak{A}\)-principal, \(\eta\)-parallel shape operator, Real submanifolds in complex manifolds, complex quadric, \(\mathfrak{A}\)-isotropic
ruled real hypersurface, $\mathfrak{A}$-isotropic, Global submanifolds, Complex conjugation, Global differential geometry of Hermitian and Kählerian manifolds, Complex quadric, $\eta$-Parallel shape operator, $\mathfrak{A}$-principal, Ruled real hypersurface, complex conjugation, \(\mathfrak{A}\)-principal, \(\eta\)-parallel shape operator, Real submanifolds in complex manifolds, complex quadric, \(\mathfrak{A}\)-isotropic
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