Abstract. In this paper we give a non-existence theorem for Hopf hypersurfaces M in complex two-plane Grassmannians G2(C m+2 ) whose normal Jacobi operatorRN is paralleland

We give some non-existence theorems for Hopf real hypersurfaces in complex two-plane Grassmannians G2(C m+2 ) with parallel structure Jacobi operator R ξ . IntroductionIn the geometry of real hypersurfaces in complex space forms or in quaternionic space forms there have been many characterizations of homogeneous hypersurfaces of type (A 1 ), (A 2 ), (B), (C), (D) and (E) in complex projective spaces P n (C), of type (A 0 ), (A 1 ), (A 2 ) and (B) in complex hyperbolic spaces H n (C) or of type (A 1 ), (A 2 ) and (B) in quaternionic projective spaces QP m , which are completely classied by Cecil and Ryan [5], Kimura [7], Berndt [2], Martinez and Pérez [9] respectively.

No abstract

We introduce the notion of generalized Tanaka-Webster connection for hypersurfaces in complex two-plane Grassmannians G 2 ðC mþ2 Þ and give a non-existence theorem for Hopf hypersurfaces in G 2 ðC mþ2 Þ with parallel shape operator in this connection.

No abstract