SEMI-SYMMETRIC STRUCTURE JACOBI OPERATOR FOR REAL HYPERSURFACES IN THE COMPLEX QUADRIC

In this paper, we introduce the notion of {\it semi-symmetric structure Jacobi operator } for Hopf real hypersufaces in the complex quad\-ric $Q^m = SO_{m+2}/SO_mSO_2$. Next we prove that there does not exist any Hopf real hypersurface in the complex quadric $Q^m = SO_{m+2}/SO_mSO_2$ with semi-symmetric structure Jacobi operator. As a corollary, we also get a non-existence property of Hopf real hypersurfaces in the complex quadric $Q^m$ with either symmetric (parallel), or recurrent structure Jacobi operator. KCI Citation Count: 0