S. H. Kon1, Tee‐How Loo1, Shiquan Ren1
1Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia
Tóm tắt
Abstract
In this paper we classify the real hypersurfaces in a non-flat complex space form with its structure Jacobi operator R
ξ satisfying (∇X
R
ξ)ξ = 0, for all vector fields X in the maximal holomorphic distribution D. With this result, we prove the non-existence of real hypersurfaces with D-parallel as well as D-recurrent structure Jacobi operator in complex projective and hyperbolic spaces. We can also prove the non-existence of real hypersurfaces with recurrent structure Jacobi operator in a non-flat complex space form as a corollary.
