Explicit formulas for biharmonic submanifolds in Sasakian space forms

D. Fetcu; C. Oniciuc

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arXiv · 0706.4160

Explicit formulas for biharmonic submanifolds in Sasakian space forms

D. Fetcu·C. Oniciuc

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Abstract

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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BibTeX RIS

D. Fetcu, C. Oniciuc. 2007-06-28. Explicit formulas for biharmonic submanifolds in Sasakian space forms. https://arxiv.org/abs/0706.4160

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