http://swrc.ontoware.org/ontology#Article
Envelopes of families of Legendre mappings in the unit tangent bundle over the Euclidean space
en
envelope
family of legendre mappings
frontal
singular solution
TAKAHASHI Masatomo
For families of hypersurfaces with singular points, a classical definition of an envelope is vague. In order to define an envelope for a family of hypersurfaces with singular points, we consider r-parameter families of frontals and of Legendre mappings in the unit tangent bundle over the Euclidean space. We define an envelope for the r-parameter family of Legendre mappings. Then the envelope is also a frontal. We investigate properties of the envelopes. As an application, we give a condition that the projection of a singular solution of a first order partial differential equation is an envelope.
Journal of Mathematical Analysis and Applications
473
1
408-420
2019-05-01
Elsevier
info:doi/10.1016/j.jmaa.2018.12.057
410
0022-247X
AA00252847
© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
application/pdf