Bifurcation and Local Rigidity of Homogeneous Solutions to the Yamabe Problem on Aloff-Wallach Spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913371357446144 |
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| author | Grama, Lino Anderson da Silva Lima, Kennerson Nascimento de Sousa |
| author_facet | Grama, Lino Anderson da Silva Lima, Kennerson Nascimento de Sousa |
| contents | We construct 1-parameter families of well-known solutions to the Yamabe problem defined on Aloff-Wallach Spaces to determine bifurcation instants for these homogeneous spaces by examining changes in the Morse index of these metrics as the parameter varies over the positive real numbers. A bifurcation point for such families is an accumulation point of other solutions to the Yamabe problem, while a local rigidity point is an isolated solution of this problem, i.e., it is not a bifurcation point. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_20345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bifurcation and Local Rigidity of Homogeneous Solutions to the Yamabe Problem on Aloff-Wallach Spaces Grama, Lino Anderson da Silva Lima, Kennerson Nascimento de Sousa Differential Geometry 53 We construct 1-parameter families of well-known solutions to the Yamabe problem defined on Aloff-Wallach Spaces to determine bifurcation instants for these homogeneous spaces by examining changes in the Morse index of these metrics as the parameter varies over the positive real numbers. A bifurcation point for such families is an accumulation point of other solutions to the Yamabe problem, while a local rigidity point is an isolated solution of this problem, i.e., it is not a bifurcation point. |
| title | Bifurcation and Local Rigidity of Homogeneous Solutions to the Yamabe Problem on Aloff-Wallach Spaces |
| topic | Differential Geometry 53 |
| url | https://arxiv.org/abs/2405.20345 |