Hiroshima Mathematical Journal
- Hiroshima Math. J.
- Volume 47, Number 1 (2017), 63-86.
On prolongations of second-order regular overdetermined systems with two independent and one dependent variables
The purpose of this paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of the rank two prolongation. Utilizing this prolongation, we characterize the type of overdetermined systems and clarify the specificity for each type. We also give systematic methods for constructing the geometric singular solutions by analyzing a decomposition of this prolongation. As an application, we determine the geometric singular solutions of Cartan’s overdetermined system.
Hiroshima Math. J., Volume 47, Number 1 (2017), 63-86.
Received: 17 September 2013
Revised: 12 November 2016
First available in Project Euclid: 13 April 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 58A15: Exterior differential systems (Cartan theory)
Secondary: 58A17: Pfaffian systems
Noda, Takahiro. On prolongations of second-order regular overdetermined systems with two independent and one dependent variables. Hiroshima Math. J. 47 (2017), no. 1, 63--86. doi:10.32917/hmj/1492048848. https://projecteuclid.org/euclid.hmj/1492048848