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談話会・数理科学講演会
過去の記録 ～05/23｜次回の予定｜今後の予定 05/24～
| 担当者 | 会田茂樹，大島芳樹，志甫淳（委員長），高田了 |
|---|---|
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index.html |
2010年10月29日(金)
16:30-17:30 数理科学研究科棟(駒場) 002号室
*** 通常とは部屋が異なります。ご注意ください ***
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Robin Graham 氏 (University of Washington)
Ambient metrics and exceptional holonomy (ENGLISH)
*** 通常とは部屋が異なります。ご注意ください ***
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Robin Graham 氏 (University of Washington)
Ambient metrics and exceptional holonomy (ENGLISH)
[ 講演概要 ]
The holonomy of a pseudo-Riemannian metric is a subgroup of the orthogonal group which measures the structure preserved by parallel translation. Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of great interest in recent years. This talk will outline a construction of metrics in dimension 7 whose holonomy is contained in the split real form of the exceptional group $G_2$. The datum for the construction is a generic real-analytic 2-plane field on a manifold of dimension 5; the metric in dimension 7 arises as the ambient metric of a conformal structure on the 5-manifold defined by Nurowski in terms of the 2-plane field.
The holonomy of a pseudo-Riemannian metric is a subgroup of the orthogonal group which measures the structure preserved by parallel translation. Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of great interest in recent years. This talk will outline a construction of metrics in dimension 7 whose holonomy is contained in the split real form of the exceptional group $G_2$. The datum for the construction is a generic real-analytic 2-plane field on a manifold of dimension 5; the metric in dimension 7 arises as the ambient metric of a conformal structure on the 5-manifold defined by Nurowski in terms of the 2-plane field.
