Quadratic Killing normal Jacobi operator for real hypersurfaces in complex Grassmannians of rank 2

摘要

In this paper, we introduce a new notion of quadratic Killing normal Jacobi operator (simply, Killing normal Jacobi operator) and its geometric meaning for real hypersurfaces in the complex Grassmannians of rank two G(2)(m+2)(c), c not equal 0. In addition, we give two classification theorems for Hopf real hypersurfaces with quadratic Killing normal Jacobi operator in complex two-plane Grassmannians of compact type and of non-compact type. (C) 2020 Elsevier B.V. All rights reserved.