Construction of normally biharmonic submanifolds
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908990117511168 |
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| author | Cherif, Ahmed Mohammed |
| author_facet | Cherif, Ahmed Mohammed |
| contents | We examine biharmonic submanifolds within warped product structures. For a submanifold $(M,g)\subset (N,h)$ and a positive smooth function $f:I\to\mathbb{R}^+$, we study the inclusion $φ:(I\times M,\widetilde{g})\to (I\times N,\overline{h})$, where $\widetilde{g}=dt^2+f^2g$ and $\overline{h}=dt^2+f^2h$. We relate the tension and bitension fields of $φ$ to the warping function and the geometry of $M$. We further characterize tangentially and normally biharmonic cases via differential conditions on $f$, and interpret these conditions in terms of the Ricci curvature of $(M,g)$ and $(I\times M,\widetilde{g})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22047 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of normally biharmonic submanifolds Cherif, Ahmed Mohammed Differential Geometry We examine biharmonic submanifolds within warped product structures. For a submanifold $(M,g)\subset (N,h)$ and a positive smooth function $f:I\to\mathbb{R}^+$, we study the inclusion $φ:(I\times M,\widetilde{g})\to (I\times N,\overline{h})$, where $\widetilde{g}=dt^2+f^2g$ and $\overline{h}=dt^2+f^2h$. We relate the tension and bitension fields of $φ$ to the warping function and the geometry of $M$. We further characterize tangentially and normally biharmonic cases via differential conditions on $f$, and interpret these conditions in terms of the Ricci curvature of $(M,g)$ and $(I\times M,\widetilde{g})$. |
| title | Construction of normally biharmonic submanifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.22047 |