On $\overline{\partial }_{b}$-harmonic maps from pseudo-Hermitian manifolds to Kähler manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912305623597056 |
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| author | Dong, Yuxin Liu, Hui Zhao, Biqiang |
| author_facet | Dong, Yuxin Liu, Hui Zhao, Biqiang |
| contents | In this paper, we consider maps from pseudo-Hermitian manifolds to Kähler manifolds and introduce partial energy functionals for these maps.
First, we obtain a foliated Lichnerowicz type result on general
pseudo-Hermitian manifolds, which generalizes a related result on Sasakian
manifolds in \cite{SSZ2013holomorphic}. Next, we investigate critical maps of the partial
energy functionals, which are referred to as $\overline{\partial }_{b}$-harmonic maps and $\partial _{b}$-harmonic maps. We give a foliated result
for both $\overline{\partial }_{b}$- and $\partial _{b}$-harmonic maps,
generalizing a foliated result of Petit \cite{Pet2002harmonic} for harmonic maps. Then we
are able to generalize Siu's holomorphicity result for harmonic maps \cite{Siu1980rigid}
to the case for $\overline{\partial }_{b}$- and $\partial _{b}$-harmonic
maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $\overline{\partial }_{b}$-harmonic maps from pseudo-Hermitian manifolds to Kähler manifolds Dong, Yuxin Liu, Hui Zhao, Biqiang Differential Geometry 53C25, 58E20 In this paper, we consider maps from pseudo-Hermitian manifolds to Kähler manifolds and introduce partial energy functionals for these maps. First, we obtain a foliated Lichnerowicz type result on general pseudo-Hermitian manifolds, which generalizes a related result on Sasakian manifolds in \cite{SSZ2013holomorphic}. Next, we investigate critical maps of the partial energy functionals, which are referred to as $\overline{\partial }_{b}$-harmonic maps and $\partial _{b}$-harmonic maps. We give a foliated result for both $\overline{\partial }_{b}$- and $\partial _{b}$-harmonic maps, generalizing a foliated result of Petit \cite{Pet2002harmonic} for harmonic maps. Then we are able to generalize Siu's holomorphicity result for harmonic maps \cite{Siu1980rigid} to the case for $\overline{\partial }_{b}$- and $\partial _{b}$-harmonic maps. |
| title | On $\overline{\partial }_{b}$-harmonic maps from pseudo-Hermitian manifolds to Kähler manifolds |
| topic | Differential Geometry 53C25, 58E20 |
| url | https://arxiv.org/abs/2504.01439 |