Horizontality with infinite complexity in the twistor spaces on tori
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911392572899328 |
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| author | Ando, Naoya Yonezaki, Anri |
| author_facet | Ando, Naoya Yonezaki, Anri |
| contents | We study the complexity of horizontality in the twistor space $\hat{E}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-definite metric over a torus. If the horizontality has finite complexity of degree $d>2$ for an element of a fiber of $\hat{E}$, then the complexity is expressed in terms of a finite subgroup of $SO(3)$ ([3]). In the present paper, we observe that if the horizontality has infinite complexity derived from one of the cases studied in [3], then the complexity is expressed by a dense subset of $S^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Horizontality with infinite complexity in the twistor spaces on tori Ando, Naoya Yonezaki, Anri Differential Geometry We study the complexity of horizontality in the twistor space $\hat{E}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-definite metric over a torus. If the horizontality has finite complexity of degree $d>2$ for an element of a fiber of $\hat{E}$, then the complexity is expressed in terms of a finite subgroup of $SO(3)$ ([3]). In the present paper, we observe that if the horizontality has infinite complexity derived from one of the cases studied in [3], then the complexity is expressed by a dense subset of $S^2$. |
| title | Horizontality with infinite complexity in the twistor spaces on tori |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2402.02748 |