Ruled Real Hypersurfaces in he Complex Quadric Kimura, Makoto Lee, Hyunjin Pérez Jiménez, Juan De Dios Suh, Young Jin $\eta$-Parallel shape operator $\mathfrak{A}$-isotropic $\mathfrak{A}$-principal Ruled real hypersurface Complex conjugation 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. 2024-01-26T07:44:15Z 2024-01-26T07:44:15Z 2021 journal article Published version: Kimura, M., Lee, H., Pérez, J.d.D. et al. Ruled Real Hypersurfaces in the Complex Quadric. J Geom Anal 31, 7989–8012 (2021). https://doi.org/10.1007/s12220-020-00564-2 https://hdl.handle.net/10481/87322 10.1007/s12220-020-00564-2 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional