| Cartan引理的推广 |
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| 引用本文： | 吴金文. Cartan引理的推广[J]. 吉首大学学报(自然科学版), 1990, 0(2) |
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| 作者姓名： | 吴金文 |
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| 作者单位： | 吉首大学数学系 |
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| 摘 要： | 本文将现代微分几何中著名的Cartan引理,推广到二次外形式空间(?)~2(V~*),得出两个定理.
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| 关 键 词： | Cartan引理 Pfaff形式 二次外形式空间 |
Generalization of Cartan''''s Lemma |
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| Wu Jinwen. Generalization of Cartan''''s Lemma[J]. Journal of Jishou University(Natural Science Edition), 1990, 0(2) |
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| Authors: | Wu Jinwen |
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| Abstract: | In this paper, we generalize the Cartan's lemma to ∧2(v*), and obtain.Theorem 1, Let w1, w2, …, wr, wr+1, …, wn be a basis and θ1, θ2,…,θr∈∧2(v*), (1≤r≤n), then ∑r wi/θi= 0 if and only if there areauvw∈F,such thatwhere a jkj + aijk- aikj = 0(1≤i,j,k≤r)andTheorem 2, Let w1, w2, …, wr∈v*(1≤r≤n) be r-linear independent pfaff forms and g∈∧2(v*) then that pfaff equation system wi= 0(i = l, 2, …, r) implys g= 0 if and only if there are θ1, θ2 , …, θx∈v* such tha |
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| Keywords: | Cartan's Iemma Pfaff form. 2-exterior form space. |
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