We shall show that the Euler characteristic form of E plays the roleof the Stiefel-Whitney characteristic form of M, and the integral formula of the Eulercharacteristic form of E is just the generalized Gauss-Bonnet formula.

• 我们同时指出:丛E的Euler示性式的积分公式正好是J.；Eells的广义Gauss-Bonnet公式。