Relative local equivalence of Engel structures
Relative local equivalence of Engel structures
复制标题
恩格尔结构的相对局部等价
DOI：
10.1007/s00209-012-1026-8
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Jiro Adachi
中科院分区：
文献类型：
--
作者：
M.Itoh;H.Satoh;Furuhata H.;Jiro Adachi
研究了相对于任意子集确定恩格尔结构胚芽的条件。我们证明了相对于任意子集的一点上的Engel结构的芽是由Engel结构本身对子集的代数限制和推导出的偶接触结构对子集的投影代数限制决定的。当子集为光滑子流形时，代数约束等价于几何约束。即使子集是光滑子流形，我们也需要一个新的更严格的概念，投影代数限制。
The conditions to determine germs of Engel structures relative to arbitrary subsets are studied. We show that germs of Engel structures at a point relative to an arbitrary subset are determined by the algebraic restrictions of the Engel structures themselves to the subset, and the projected algebraic restrictions of the derived even-contact structures to the subset. When the subset is a smooth submanifold, algebraic restriction is equivalent to geometric restriction. Even when the subset is a smooth submanifold, we need a new stricter notion, projected algebraic restriction.