Tokyo Journal of Mathematics

Rank Two Prolongations of Second-order PDE and Geometric Singular Solutions

Takahiro NODA and Kazuhiro SHIBUYA

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We study geometric structures of rank two prolongations of implicit second-order partial differential equations (PDEs) for two independent and one dependent variables and characterize the type of these PDEs by the topology of fibers of the rank two prolongations. Moreover, by using properties of these prolongations, we give explicit expressions of geometric singular solutions of second-order PDEs from the point of view of contact geometry of second order.

Article information

Tokyo J. Math., Volume 37, Number 1 (2014), 73-110.

First available in Project Euclid: 28 July 2014

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Zentralblatt MATH identifier

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


NODA, Takahiro; SHIBUYA, Kazuhiro. Rank Two Prolongations of Second-order PDE and Geometric Singular Solutions. Tokyo J. Math. 37 (2014), no. 1, 73--110. doi:10.3836/tjm/1406552432.

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