Real Hypersurfaces with Pseudo-parallel Normal Jacobi Operator in Complex Two-Plane Grassmannians

Abstract

The objective of the present paper is to prove the non-existence
of real hypersurface with pseudo-parallel normal Jacobi operator in complex
two-plane Grassmannians. As a corollary, we show that there does not exist
any real hypersurface with semi-parallel or recurrent normal Jacobi operator
in complex two-plane Grassmannians. This answers a question considered in
[Monatsh Math, 172 (2013), 167-178] in negative.