On critical maps of the horizontal energy functional between Riemannian foliations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912305644568576 |
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| author | Chong, Tian Dong, Yuxin Huang, Xin Liu, Hui |
| author_facet | Chong, Tian Dong, Yuxin Huang, Xin Liu, Hui |
| contents | In this paper, we consider critical points of the
horizontal energy $E_{\HH}(f)$ for a smooth map $f$ between two Riemannian
foliations. These critical points are referred to as horizontally harmonic
maps. In particular, if the maps are foliated, they become transversally
harmonic maps. By utilizing the stress-energy tensor, we establish some
monotonicity formulas for horizontally harmonic maps from Euclidean spaces,
the quotients $K_{m}$ of Heisenberg groups and also for transversally
harmonic maps from Riemannian foliations with appropriate curvature pinching
conditions. Finally, we give Jin-type theorems for either horizontally
harmonic maps or transversally harmonic maps under some asymptotic
conditions at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On critical maps of the horizontal energy functional between Riemannian foliations Chong, Tian Dong, Yuxin Huang, Xin Liu, Hui Differential Geometry 58E20, 53C12, 53C43 In this paper, we consider critical points of the horizontal energy $E_{\HH}(f)$ for a smooth map $f$ between two Riemannian foliations. These critical points are referred to as horizontally harmonic maps. In particular, if the maps are foliated, they become transversally harmonic maps. By utilizing the stress-energy tensor, we establish some monotonicity formulas for horizontally harmonic maps from Euclidean spaces, the quotients $K_{m}$ of Heisenberg groups and also for transversally harmonic maps from Riemannian foliations with appropriate curvature pinching conditions. Finally, we give Jin-type theorems for either horizontally harmonic maps or transversally harmonic maps under some asymptotic conditions at infinity. |
| title | On critical maps of the horizontal energy functional between Riemannian foliations |
| topic | Differential Geometry 58E20, 53C12, 53C43 |
| url | https://arxiv.org/abs/2504.01498 |