Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting structure Jacobi operators

Abstract

In this paper, we introduce a new commuting condition between the structure Jacobi operator and symmetric (1,1)-type tensor field $T$, that is, $R_{\xi }\varphi T=T{R}_{\xi }\varphi$, where $T=A$ or $T=S$ for Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians. By using simultaneous diagonalzation for commuting symmetric operators, we give a complete classification of real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting condition respectively.

arXiv commentarXiv admin note: text overlap with arXiv:1409.6387, arXiv:1310.5436