Abstract

We classify all biharmonic Legendre curves in a Sasakian space form and obtain their explicit parametric equations in the (2n + 1)-dimensional unit sphere endowed with the canonical and deformed Sasakian structures defined by Tanno. We also show that, under the flow-action of the characteristic vector field, a biharmonic integral submanifold becomes a biharmonic anti-invariant submanifold. Then, we obtain new examples of biharmonic submanifolds in the Euclidean sphere S⁷.

Keywords

biharmonic submanifold, Sasakian space form, Legendre curve, integral submanifold

Mathematical Subject Classification

Primary: 53B25, 53C42

Milestones

Received: 2 July 2008
Accepted: 25 November 2008
Published: 2 March 2009

Authors