Explicit formulas for biharmonic submanifolds in Sasakian space forms

Dorel Fetcu and Cezar Oniciuc

Vol. 240 (2009), No. 1, 85–107

DOI: 10.2140/pjm.2009.240.85

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 2000

Primary: 53B25, 53C42

Milestones

Received: 2 July 2008

Accepted: 25 November 2008

Published: 2 March 2009