# 达布定理 (微分几何)

## 定理的陈述和第一个推论

θ ∧ (dθ)p = 0 ，

θ = x1 dy1 + ... + xp : θ = x1 dy1 + ... + xp dyp + dxp+1

dyp。 另一个方面，如果任一点有

θ ∧ (dθ)p ≠ 0 任何处,

θ = x1 dy1 + ... + xp dyp + dxp+1.

θ = x1 dy1 + ... + xm dym

ω = dθ = dx1 ∧ dy1 + ... + dxm ∧ dym

${\displaystyle \omega =\phi ^{*}\omega _{0}\,}$

## 注释

1. ^ Darboux (1882).
2. ^ Pfaff (1814-1815).
3. ^ Sternberg (1964) p. 140-141.
4. ^ Cf. with McDuff and Salamon (1998) p. 96.

## 参考文献

• Darboux, Gaston. Sur le problème de Pfaff. Bull. Sci. Math. 1882, 6: 14–36, 49–68. 外部链接存在于|title= (帮助)
• Pfaff, Johann Friedrich. Methodus generalis, aequationes differentiarum partialium nec non aequationes differentiales vulgates, ultrasque primi ordinis, inter quotcunque variables, complete integrandi. Abhandlungen der Königlichen Akademie der Wissenschaften in Berlin. 1814–1815: 76–136.
• Sternberg, Shlomo. Lectures on Differential Geometry. Prentice Hall. 1964.
• McDuff, D. and Salamon, D. Introduction to Symplectic Topology. Oxford University Press. 1998. ISBN 0-19-850451-9.