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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2406.03828 |
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| _version_ | 1866929459794280448 |
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| author | Berestovskii, V. N. |
| author_facet | Berestovskii, V. N. |
| contents | We discuss models of the Gödel Universe as Lie groups with left-invariant Lorentz metric for two simply connected four-dimensional Lie groups, the Iwasawa decomposition for semisimple Lie groups, and left-invariant Lorentz metric on ${\rm SL}(2,\mathbb{R})$, following K.-H.~Neeb. Also we show that the isometry between two non-isomorphic sub-Riemannian Lie group, constructed by A.~Agrachev and D.~Barilari, is induced by some Iwasawa decomposition of ${\rm SL}(2,\mathbb{R})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Gödel Universe as a Lie group with left-invariant Lorentz metric and\newline the Iwasawa decomposition Berestovskii, V. N. Differential Geometry 83C20, 53C50, 53C30, 49J15 We discuss models of the Gödel Universe as Lie groups with left-invariant Lorentz metric for two simply connected four-dimensional Lie groups, the Iwasawa decomposition for semisimple Lie groups, and left-invariant Lorentz metric on ${\rm SL}(2,\mathbb{R})$, following K.-H.~Neeb. Also we show that the isometry between two non-isomorphic sub-Riemannian Lie group, constructed by A.~Agrachev and D.~Barilari, is induced by some Iwasawa decomposition of ${\rm SL}(2,\mathbb{R})$. |
| title | The Gödel Universe as a Lie group with left-invariant Lorentz metric and\newline the Iwasawa decomposition |
| topic | Differential Geometry 83C20, 53C50, 53C30, 49J15 |
| url | https://arxiv.org/abs/2406.03828 |