The Geometry of Loop Spaces IV: Closed Sasakian Manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916706182496256 |
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| author | Maeda, Yoshiaki Rosenberg, Steven |
| author_facet | Maeda, Yoshiaki Rosenberg, Steven |
| contents | We prove that a closed regular $(4k+1)$-Sasakian manifold $(M,h_0)$ admits a family of non-isometric metrics $h_ρ, ρ\geq 0,$ such that $π_1({\rm Isom}(M, h_ρ))$, the fundamental group of the isometry group, is infinite for $ρ>0.$ For $M= S^{4k+1}$, this result holds for all $ρ>0$, but fails at $ρ=0.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16743 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Geometry of Loop Spaces IV: Closed Sasakian Manifolds Maeda, Yoshiaki Rosenberg, Steven Differential Geometry 53D35 We prove that a closed regular $(4k+1)$-Sasakian manifold $(M,h_0)$ admits a family of non-isometric metrics $h_ρ, ρ\geq 0,$ such that $π_1({\rm Isom}(M, h_ρ))$, the fundamental group of the isometry group, is infinite for $ρ>0.$ For $M= S^{4k+1}$, this result holds for all $ρ>0$, but fails at $ρ=0.$ |
| title | The Geometry of Loop Spaces IV: Closed Sasakian Manifolds |
| topic | Differential Geometry 53D35 |
| url | https://arxiv.org/abs/2412.16743 |