论文标题
一系列Banach束和Darboux定理的一系列兼容弱符号形式的投影极限
Projective limit of a sequence of compatible weak symplectic forms on a sequence of Banach bundles and Darboux Theorem
论文作者
论文摘要
考虑到Banach束的投影序列，每个束都提供了弱的互合式形式，我们寻找条件，在这些条件下，弱符号形式的相应序列在投影限制束上产生了弱的符号形式。然后，我们将此结果应用于Banach歧管的投影限制的切线束。这自然会导致询问在Banach歧管的投影限制上，Darboux定理在遵守情况下也是如此。我们将提供一些必要的和一些足够的条件，以使这样的结果为真。然后，我们讨论为什么Moser的方法无法在没有非常强烈的条件（例如Kumar的结果）的情况下对Banach弱的拟合Banach歧管的投影限制（[17]）起作用（[17]）。特别是，我们举了一个示例，说明了弱符号Banach流形的投影序列，在每个歧管上，darboux定理是真实的，但在这些歧管的投影限制上并不是真实的。
Given a projective sequence of Banach bundles, each one provided with a of weak symplectic form, we look for conditions under which, the corresponding sequence of weak symplectic forms gives rise to weak symplectic form on the projective limit bundle. Then we apply this results to the tangent bundle of a projective limit of Banach manifolds. This naturally leads to ask about conditions under which the Darboux Theorem is also true on the projective limit of Banach manifolds. We will give some necessary and some sufficient conditions so that such a result is true. Then we discuss why, in general, the Moser's method can not work on projective limit of Banach weak symplectic Banach manifolds without very strong conditions like Kumar 's results ([17]). In particular we give an example of a projective sequence of weak symplectic Banach manifolds on which the Darboux Theorem is true on each manifold, but is not true on the projective limit of these manifolds.
