Novikov-type inequalities for vector fields with non-isolated zero points
Novikov-type inequalities for vector fields with non-isolated zero points
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DOI：
10.2140/pjm.2001.201.107
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发表时间：
2001-11
影响因子：
0.6
通讯作者：
Huitao Feng;Enli Guo
中科院分区：
文献类型：
--
作者：
Huitao Feng;Enli Guo
在文章[5]中，Shubin给出了对具有孤立零点的向量场的Novikov不等式的详细处理，对此Novikov在[4]的附录中给出了一个证明。因此，给出了这些向量场的Hopf指数定理的直接解析证明。另一方面，Braverman和Farber[2]得到了一些具有非孤立零点的闭1型的novikov型不等式。在[3]中，我们通过构造一个超扭曲的Dirac算子，将Shubin[5]的一些结果推广到与基流形相同维数的一般定向实向量束的截截面上。本文研究了具有非孤立零点的向量场的情况。更精确地说，设X是一个维数为n的封闭、定向、连通的黎曼流形，设v是X上的一个向量场。设Y = {Y∈X | v(Y) = 0}。
In the article [5], Shubin presented a detailed treatment of the Novikov inequalities for vector fields with isolated zero points, to which Novikov sketched a proof in the appendix to [4]. As a consequence, a direct analytic proof of the Hopf index theorem for these vector fields is given. On the other hand, Braverman and Farber [2] obtained some Novikov-type inequalities for closed 1-forms with non-isolated zero points. In [3], we extended some results of Shubin [5] to a transversal section of a general oriented real vector bundle with the same dimension as its base manifold by constructing a super-twisted Dirac operator. In this paper, we study the case of vector fields with non-isolated zero points. More precisely, let X be a closed, oriented and connected Riemannian manifold of dimension n and let v be a vector field on X. Set Y = {y ∈ X | v(y) = 0}.