Second-order generalized Monge--Amp\`ere equations on a plane and its geometric singular solutions
Differential Geometry
2021-11-16 v2
Abstract
In the present paper, we study some generalized Monge--Amp\`ere equations in terms of special exterior differential systems on a jet space. Moreover, we construct geometric singular solutions of the generalized Monge--Amp\`ere equations by using the method of Cauchy characteristics. Furthermore, we give criteria for geometric singular solutions to be right-left equivalent to the cuspidal edge, swallowtail and butterfly.
Keywords
Cite
@article{arxiv.2111.06695,
title = {Second-order generalized Monge--Amp\`ere equations on a plane and its geometric singular solutions},
author = {Masahiro Kawamata},
journal= {arXiv preprint arXiv:2111.06695},
year = {2021}
}