The Hitchin index in cohomogeneity one nearly Kähler structures
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913605507612672 |
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| author | Solé-Farré, Enric |
| author_facet | Solé-Farré, Enric |
| contents | Nearly Kähler and Einstein structures admit a variational characterization, where the second variation is associated with a strongly elliptic operator. This allows us to associate a Morse-like index to each structure. Our study focuses on how these indices behave under the assumption that the nearly Kähler structure admits a cohomogeneity one action. Specifically, we investigate elements of the index that also exhibit cohomogeneity one symmetry, reducing the analysis to an ODE eigenvalue problem.
We apply our discussion to the two inhomogeneous examples constructed by Foscolo and Haskins. We obtain non-trivial lower bounds on the Hitchin index and Einstein co-index for the inhomogeneous nearly Kähler structure on $S^3\times S^3$, answering a question of Karigiannis and Lotay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21106 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hitchin index in cohomogeneity one nearly Kähler structures Solé-Farré, Enric Differential Geometry 53C10, 53C25, 53C29, 53C55 Nearly Kähler and Einstein structures admit a variational characterization, where the second variation is associated with a strongly elliptic operator. This allows us to associate a Morse-like index to each structure. Our study focuses on how these indices behave under the assumption that the nearly Kähler structure admits a cohomogeneity one action. Specifically, we investigate elements of the index that also exhibit cohomogeneity one symmetry, reducing the analysis to an ODE eigenvalue problem. We apply our discussion to the two inhomogeneous examples constructed by Foscolo and Haskins. We obtain non-trivial lower bounds on the Hitchin index and Einstein co-index for the inhomogeneous nearly Kähler structure on $S^3\times S^3$, answering a question of Karigiannis and Lotay. |
| title | The Hitchin index in cohomogeneity one nearly Kähler structures |
| topic | Differential Geometry 53C10, 53C25, 53C29, 53C55 |
| url | https://arxiv.org/abs/2410.21106 |