Hill, Nurowski: Differential Equations and Para-CR Structures

Hill, C. Denson and Nurowski, Paweł:
Differential Equations and Para-CR Structures
Bollettino dell'Unione Matematica Italiana Serie 9 3 (2010), fasc. n.1, p. 25-91, (English)
pdf (844 Kb), djvu (612 Kb). | MR 2605912 | Zbl 1206.58001

Sunto

We study the local geometry of n dimensional manifolds which are equipped with two integrable distributions, one of dimension $r$ and one of dimension $s$, where $r$ and $s$ are allowed to be unequal. We call them para-CR structures of type $(k,r,s)$, with $k = n - r - s \ge 0$ being the para-CR codimension. When $r = s$ they are the real analogues of CR structures. In the general case these structures are the natural geometric setting in which to discuss the geometry of systems of ODE's, as well as the geometry of systems of PDE's of finite type. For particular small values of $k,r,s$ we determine the basic local invariants of such structures.

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Referenze Bibliografiche