Semisymmetric hypersurfaces in complex hyperbolic two-plane Grassmannians

Authors: DOO HYUN HWANG, CHANGHWA WOO

Abstract: In this paper, we introduce new notions of symmetric operators such as semisymmetric shape operator and structure Jacobi operator in complex hyperbolic two-plane Grassmannians. Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$ with such notions.

Keywords: Real hypersurfaces, complex hyperbolic two-plane Grassmannians, Hopf hypersurface, semisymmetric shape operator, semisymmetric structure Jacobi operator

Full Text: PDF