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複素解析幾何セミナー
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
| 開催情報 | 月曜日 10:30～12:00 数理科学研究科棟(駒場) 128号室 |
|---|---|
| 担当者 | 平地 健吾, 高山 茂晴 |
2017年03月06日(月)
10:00-11:30 数理科学研究科棟(駒場) 128号室
いつもと時間が異なります。
Vladimir Matveev 氏 (University of Jena)
Projective and c-projective metric geometries: why they are so similar (ENGLISH)
いつもと時間が異なります。
Vladimir Matveev 氏 (University of Jena)
Projective and c-projective metric geometries: why they are so similar (ENGLISH)
[ 講演概要 ]
I will show an unexpected application of the standard techniques of integrable systems in projective and c-projective geometry (I will explain what they are and why they were studied). I will show that c-projectively equivalent metrics on a closed manifold generate a commutative isometric $\mathbb{R}^k$-action on the manifold. The quotients of the metrics w.r.t. this action are projectively equivalent, and the initial metrics can be uniquely reconstructed by the quotients. This gives an almost algorithmic way to obtain results in c-projective geometry starting with results in much better developed projective geometry. I will give many application of this algorithmic way including local description, proof of Yano-Obata conjecture for metrics of arbitrary signature, and describe the topology of closed manifolds admitting strictly nonproportional c-projectively equivalent metrics.
Most results are parts of two projects: one is joint with D. Calderbank, M. Eastwood and K. Neusser, and another is joint with A. Bolsinov and S. Rosemann.
I will show an unexpected application of the standard techniques of integrable systems in projective and c-projective geometry (I will explain what they are and why they were studied). I will show that c-projectively equivalent metrics on a closed manifold generate a commutative isometric $\mathbb{R}^k$-action on the manifold. The quotients of the metrics w.r.t. this action are projectively equivalent, and the initial metrics can be uniquely reconstructed by the quotients. This gives an almost algorithmic way to obtain results in c-projective geometry starting with results in much better developed projective geometry. I will give many application of this algorithmic way including local description, proof of Yano-Obata conjecture for metrics of arbitrary signature, and describe the topology of closed manifolds admitting strictly nonproportional c-projectively equivalent metrics.
Most results are parts of two projects: one is joint with D. Calderbank, M. Eastwood and K. Neusser, and another is joint with A. Bolsinov and S. Rosemann.
