Hiroshima Mathematical Journal

On prolongations of second-order regular overdetermined systems with two independent and one dependent variables

Takahiro Noda

Full-text: Open access

Abstract

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.

Article information

Source
Hiroshima Math. J., Volume 47, Number 1 (2017), 63-86.

Dates
Received: 17 September 2013
Revised: 12 November 2016
First available in Project Euclid: 13 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1492048848

Digital Object Identifier
doi:10.32917/hmj/1492048848

Mathematical Reviews number (MathSciNet)
MR3634262

Zentralblatt MATH identifier
1373.35205

Subjects
Primary: 58A15: Exterior differential systems (Cartan theory)
Secondary: 58A17: Pfaffian systems

Keywords
Regular overdetermined systems of second order differential systems rank two prolongations geometric singular solutions

Citation

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


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