Characterization of Biharmonic Hypersurface

Abstract

The main purpose of this paper is to study biharmonic hypersurface in a quasi-paraSasakian manifold $\mathbb{Q}^{2m+1}$. Biharmonic hypersurfaces are special cases of biharmonic maps and biharmonic maps are the critical points of the bienergy functional. The condition of biharmonicity for non-degenerate hypersurfaces in $\mathbb{Q}^{2m+1}$ is investigated for both cases: either the characteristic vector field of $\mathbb{Q}^{2m+1}$ is the unit normal vector field to the hypersurface or it belongs to the tangent space of the hypersurface. Some relevant examples are also illustrated.

Keywords

• biharmonic map
• biharmonic hypersurface
• quasi-parasasakian manifold