On the geometry of biharmonic submanifolds in Sasakian space forms. (English) Zbl 1201.53062

The authors recollect the concept of harmonic and biharmonic mappings of Riemannian Manifolds as well. Since all harmonic maps are biharmonic they are interested in studying those which are biharmonic but non-harmonic, called proper-biharmonic maps. They classify all proper-biharmonic Legendre curves in Sasakian space form and point out some of their geometric properties. Then they provide a method for constructing anti-invariant properbiharmonic submanifolds in the Sasakian space forms. Finally, using the Bootby-Wang fibration, they determine all proper-biharmonic Hopf cylinders over homogeneous real hypersurfaces in complex projective spaces.


53C40 Global submanifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C43 Differential geometric aspects of harmonic maps