Tee-How Loo

On characterizations of real hypersurfaces in a complex space form with eta-parallel shape operator.

In this paper, we study real hypersurfaces in a non-flat complex space form with n-parallel shape operator. Several partial characterizations of these real of these real hypersurfaces are obtained.

Real hypersurfaces in a complex space form with a condition on the structure Jacobi operator

In this paper we classify the real hypersurfaces in a non-flat complex space form with its structure Jacobi operator Rξ satisfying (∇XRξ)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.

Hopf Hypersurfaces in Complex Grassmannians of Rank Two

In this paper, we study real hypersurfaces in complex Grassmannians of rank two. First, the nonexistence of mixed foliate real hypersurfaces is proven. With this result, we show that for Hopf hypersurfaces in complex Grassmannians of rank two, the Reeb principal curvature is constant along integral curves of the Reeb vector field. As a result the classification of contact real hypersurfaces is obtained. We also introduce the notion of q-umbilical real hypersurfaces in complex Grassmannians of rank two and obtain a classification of such real hypersurfaces.