Structure Lie operator on real hypersurfaces of complex two-plane Grassmannians
Volume 170 / 2022
Colloquium Mathematicum 170 (2022), 315-320
MSC: Primary 53C15; Secondary 53B25, 53D15.
DOI: 10.4064/cm8558-1-2022
Published online: 27 June 2022
Abstract
It is proved that on a real hypersurface $M$ in the complex two-plane Grassmannian $G_2(\mathbb {C}^{m+2})$, the structure Lie operator is parallel if and only if $M$ is an open part of a tube around a totally geodesic $G_2(\mathbb {C}^{m+1})$ in $G_2(\mathbb {C}^{m+2})$.
