陳-高斯-博内定理

This article "陳-高斯-博内定理" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:陳-高斯-博内定理. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one. 在幾何、拓撲中，陳定理，又稱為陳公式或陳–高斯–博内定理，以陳省身（1945）、高斯、博内命名，是高斯-博内公式的高維推廣。^[1]

陳定理成立於偶數維數閉黎曼流形，說歐拉示性數可以表達爲曲率多項式的積分。^[1]

定理[编辑]

陳公式是^[2]^[3]

$\chi (M)=\int _{M}e(\Omega )$

$e(\Omega )={\frac {1}{(2\pi )^{n}}}{\text{Pf}}(\Omega )$

${\mbox{Pf}}(\Omega )$ 是普法夫值。

M是紧、可定向、无边界的 2n-维黎曼流形。

例如在四維空間：

\chi (M)={\frac {1}{32\pi ^{2}}}\int _{M}\left(|{\text{Riem}}|^{2}-4|{\text{Ric}}|^{2}+R^{2}\right)d\mu

This article "陳-高斯-博内定理" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:陳-高斯-博内定理. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.