Explicit formulas for biharmonic submanifolds in Sasakian space forms

Details Explicit formulas for biharmonic submanifolds in Sasakian space forms Explicit formulas for biharmonic submanifolds in Sasakian space forms

2007-06-28

arxiv.org/abs/0706.4160v1

Mathematics

Differential Geometry

17 pages

Scientific paper

We classify the 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. Then, composing with the flow of the Reeb vector field, we transform a biharmonic integral submanifold into a biharmonic anti-invariant submanifold. Using this method we obtain new examples of biharmonic submanifolds in spheres and, in particular, in $\mathbb{S}^{7}$.

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