Normal-Yang-Mills and Tangent-Yang-Mills submanifolds
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918467846799360 |
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| author | Ge, Jianquan Xiao, Lixin Zhang, Wenjin |
| author_facet | Ge, Jianquan Xiao, Lixin Zhang, Wenjin |
| contents | This paper investigates the variational problems associated with the $L^2$-norms of the normal and tangent curvature tensors for submanifolds immersed in a unit sphere. We define the critical points of these functionals under normal variations as Normal-Yang-Mills and Tangent-Yang-Mills submanifolds, for which we explicitly establish the Euler-Lagrange equations in terms of the second fundamental form. Furthermore, by investigating the focal submanifolds of OT-FKM isoparametric hypersurfaces, we construct infinitely many non-trivial examples of both Normal-Yang-Mills and Tangent-Yang-Mills submanifolds. Notably, the curvature tensors of these examples generally do not satisfy the classical Yang-Mills equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23207 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Normal-Yang-Mills and Tangent-Yang-Mills submanifolds Ge, Jianquan Xiao, Lixin Zhang, Wenjin Differential Geometry 53C40, 53C42, 58E15, 53C07 This paper investigates the variational problems associated with the $L^2$-norms of the normal and tangent curvature tensors for submanifolds immersed in a unit sphere. We define the critical points of these functionals under normal variations as Normal-Yang-Mills and Tangent-Yang-Mills submanifolds, for which we explicitly establish the Euler-Lagrange equations in terms of the second fundamental form. Furthermore, by investigating the focal submanifolds of OT-FKM isoparametric hypersurfaces, we construct infinitely many non-trivial examples of both Normal-Yang-Mills and Tangent-Yang-Mills submanifolds. Notably, the curvature tensors of these examples generally do not satisfy the classical Yang-Mills equations. |
| title | Normal-Yang-Mills and Tangent-Yang-Mills submanifolds |
| topic | Differential Geometry 53C40, 53C42, 58E15, 53C07 |
| url | https://arxiv.org/abs/2604.23207 |