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Lie群論・表現論セミナー
過去の記録 ～10/04｜次回の予定｜今後の予定 10/05～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 小林俊行 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
2011年05月24日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
椋野純一 氏 (名古屋大学)
Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)
椋野純一 氏 (名古屋大学)
Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)
[ 講演概要 ]
If a homogeneous space $G/H$ is acted properly discontinuously
upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a
Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.
It follows that a compact Clifford--Klein form of the de Sitter space never exists.
In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.
If a homogeneous space $G/H$ is acted properly discontinuously
upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a
Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.
It follows that a compact Clifford--Klein form of the de Sitter space never exists.
In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.
