| 定向微分流形上Stiefel-Whitney示性类的积分公式 |
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| 引用本文： | 梅向明.定向微分流形上Stiefel-Whitney示性类的积分公式[J].首都师范大学学报(自然科学版),1993(3). |
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| 作者姓名： | 梅向明 |
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| 作者单位： | 首都师范大学数学系 |
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| 摘 要： | 命M是一个定向微分流形,T(M)是它的切丛,E是T(M)的一个子矢丛。我们将指出:矢丛E的Euler示性式扮演了流形M的Stiefel-Whitney示性式的角色,不过这个示性式积分时必须mod.2计算。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。
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| 关 键 词： | 定向微分流形 Stiefel-Whitney示性类 Euler示性式 |
The Integral Formulas of Stiefel-Whitney Classes on an Oriented Differentiable Manifold |
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| Mei Xiangming.The Integral Formulas of Stiefel-Whitney Classes on an Oriented Differentiable Manifold[J].Journal of Capital Normal University(Natural Science Edition),1993(3). |
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| Authors: | Mei Xiangming |
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| Institution: | Mei Xiangming Department of Mathematics,Capital Normal University |
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| Abstract: | Let M be an oriented differentiable manifold, T(M) be its tangent bundle, and E is asubbundle of T(M). 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. |
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| Keywords: | the oriented differentiable manifold Stiefel-Whitney characteristic form Euler characteristic form |
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