Biharmonic hypersurfaces in Sasakian space forms

On the Geometry of Biharmonic Submanifolds in Sasakian Space Forms

“…In [17] we obtained a geometric characterization of biharmonic Hopf cylinders of any codimension in an arbitrary Sasakian space form. A special case of our result is the case whenM is a hypersurface.…”

“…By using Takagi's result we classified in [17] the biharmonic Hopf cylinders M = π −1 (M ) in a Sasakian space form N 2n+1 over homogeneous real hypersurfaces in CP n , n > 1. …”

On Biharmonic Legendre curves in $S$-space forms

“…Biharmonic submanifolds have been studied by many geometers. For example, see [2], [3], [7], [8], [11], [12], [13], [14], [15], [18], [20], [21], [22], and the references therein. In a different setting, in [9], Chen defined a biharmonic submanifold M ⊂ E n of the Euclidean space as its mean curvature vector field H satisfies ∆H = 0 , where ∆ is the Laplacian.…”

Harmonic and Biharmonic Maps at Iaşi

“…The Hopf fibration π : S 2n+1 → CP n is a well-known example of Boothby-Wang fibration and, using the Takagi list (see [62]), all proper-biharmonic Hopf cylinders over homogeneous real hypersurfaces in the complex projective space CP n were given (see [31]). …”

“…After space forms, a series of non-constant sectional curvature spaces were considered as ambient spaces for the study of proper-biharmonic submanifolds (see, for example, [4,23,30,31,35,36,54,58,61]). In this respect, one of the research directions was the study of proper-biharmonic submanifolds in Sasakian space forms.…”