| 翻訳と辞書 |
| Fedosov manifold ： ウィキペディア英語版 |
Fedosov manifold
In mathematics, a Fedosov manifold is a symplectic manifold with a compatible torsion-free connection, that is, a triple (''M'', ω, ∇), where (''M'', ω) is a symplectic manifold (i.e., ω is a symplectic form, a non-degenerate closed exterior 2-form, on a ''C''∞-manifold ''M''), and ∇ is a symplectic torsion-free connection on ''M''. (A connection ∇ is called compatible or symplectic if ''X'' ⋅ ω(''Y,Z'') = ω(∇''X''''Y'',''Z'') + ω(''Y'',∇''X''''Z'') for all vector fields ''X,Y,Z'' ∈ Γ(T''M''). In other words, the symplectic form is parallel with respect to the connection, i.e., its covariant derivative vanishes.) Note that every symplectic manifold admits a symplectic torsion-free connection. Cover the manifold with Darboux charts and on each chart define a connection ∇ with Christoffel symbol . Then choose a partition of unity (subordinate to the cover) and glue the local connections together to a global connection which still preserves the symplectic form. The famous result of Boris Vasilievich Fedosov gives a canonical deformation quantization of a Fedosov manifold.
==References==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Fedosov manifold」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|