Geometry of Harmonic Identity Maps
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866929657569345536 |
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| author | Benkartab, Aicha Cherif, Ahmed Mohammed |
| author_facet | Benkartab, Aicha Cherif, Ahmed Mohammed |
| contents | An identity map $(M,g)\longrightarrow(M,g)$ is a harmonic from a Riemannian manifold $(M,g)$ onto itself. In this paper, we study the harmonicity of identity maps $(M,g)\longrightarrow(M,g-df\otimes df)$ and $(M,g-df\otimes df)\longrightarrow(M,g)$ where $f$ is a smooth function with gradient norm $<1$ on $(M,g)$. We construct new examples of identity harmonic maps. We define a symmetric tensor field on $M$ whose properties are related to the harmonicity of these identity maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry of Harmonic Identity Maps Benkartab, Aicha Cherif, Ahmed Mohammed Differential Geometry An identity map $(M,g)\longrightarrow(M,g)$ is a harmonic from a Riemannian manifold $(M,g)$ onto itself. In this paper, we study the harmonicity of identity maps $(M,g)\longrightarrow(M,g-df\otimes df)$ and $(M,g-df\otimes df)\longrightarrow(M,g)$ where $f$ is a smooth function with gradient norm $<1$ on $(M,g)$. We construct new examples of identity harmonic maps. We define a symmetric tensor field on $M$ whose properties are related to the harmonicity of these identity maps. |
| title | Geometry of Harmonic Identity Maps |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.01804 |