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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.19891 |
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| _version_ | 1866909442302279680 |
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| author | Niedzialomski, Kamil Niedzialomska, Malgorzata |
| author_facet | Niedzialomski, Kamil Niedzialomska, Malgorzata |
| contents | Let $(M,g)$ be a Riemannian manifold, $L(M)$ be its frame bundle, $O(M)$ its orthonormal frame bundle. For a distribution $D$ on $M$ we define a subbundle $L(D)\subset L(M)$ or $O(D)\subset O(M)$ in a natural way. This allows us to consider a lift $Lφ$ of a map $φ:M\to N$ not necessarily being a local diffeomorphism. More precisely, if $φ:M\to N$ is a submersion, then $Lφ:L(\mathcal{H}^φ)\to L(N)$ or $Lφ:O(\mathcal{H}^φ)\to L(N)$, where $\mathcal{H}^φ$ is a horizontal distribution of $φ$. Equipping $L(M)$ and $L(N)$ with the Mok metrics, we study conformality and harmonicity of lifts $Lφ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lifts of maps to frame bundles Niedzialomski, Kamil Niedzialomska, Malgorzata Differential Geometry Let $(M,g)$ be a Riemannian manifold, $L(M)$ be its frame bundle, $O(M)$ its orthonormal frame bundle. For a distribution $D$ on $M$ we define a subbundle $L(D)\subset L(M)$ or $O(D)\subset O(M)$ in a natural way. This allows us to consider a lift $Lφ$ of a map $φ:M\to N$ not necessarily being a local diffeomorphism. More precisely, if $φ:M\to N$ is a submersion, then $Lφ:L(\mathcal{H}^φ)\to L(N)$ or $Lφ:O(\mathcal{H}^φ)\to L(N)$, where $\mathcal{H}^φ$ is a horizontal distribution of $φ$. Equipping $L(M)$ and $L(N)$ with the Mok metrics, we study conformality and harmonicity of lifts $Lφ$. |
| title | Lifts of maps to frame bundles |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.19891 |