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トポロジー火曜セミナー
過去の記録 ～04/25｜次回の予定｜今後の予定 04/26～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也 |
| セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2020年01月14日(火)
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
茅原 涼平 氏 (東京大学大学院数理科学研究科)
SO(3)-invariant G2-geometry (JAPANESE)
Tea: Common Room 16:30-17:00
茅原 涼平 氏 (東京大学大学院数理科学研究科)
SO(3)-invariant G2-geometry (JAPANESE)
[ 講演概要 ]
Berger's classification of holonomy groups of Riemannian manifolds includes exceptional cases of the Lie groups G2 and Spin(7). Many authors have studied G2- and Spin(7)-manifolds with torus symmetry. In this talk, we generalize the celebrated examples due to Bryant and Salamon and study G2-manifolds with SO(3)-symmetry. Such torsion-free G2-structures are described as a dynamical system of SU(3)-structures on an SO(3)-fibration over a 3-manifold. As a main result, we reduce this system into a constrained Hamiltonian dynamical system on the cotangent bundle over the space of all Riemannian metrics on the 3-manifold. The Hamiltonian function is very similar to that of the Hamiltonian formulation of general relativity.
Berger's classification of holonomy groups of Riemannian manifolds includes exceptional cases of the Lie groups G2 and Spin(7). Many authors have studied G2- and Spin(7)-manifolds with torus symmetry. In this talk, we generalize the celebrated examples due to Bryant and Salamon and study G2-manifolds with SO(3)-symmetry. Such torsion-free G2-structures are described as a dynamical system of SU(3)-structures on an SO(3)-fibration over a 3-manifold. As a main result, we reduce this system into a constrained Hamiltonian dynamical system on the cotangent bundle over the space of all Riemannian metrics on the 3-manifold. The Hamiltonian function is very similar to that of the Hamiltonian formulation of general relativity.
