Poincaré-invariant structures in the solution manifold of a nonlinear wave equation.

Segal, Irving E.. "Poincaré-invariant structures in the solution manifold of a nonlinear wave equation.." Revista Matemática Iberoamericana 2.1-2 (1986): 99-104. <http://eudml.org/doc/39304>.

@article{Segal1986,
abstract = {The solution manifold M of the equation ⎯φ + gφ3 = 0 in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on M that is Poincaré invariant. In the vanishing curvature case g = 0 the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal space-time.},
author = {Segal, Irving E.},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuaciones diferenciales en derivadas parciales; Variedades complejas; Variedad riemanniana; nonlinear wave equation; solution manifold; Poincaré invariance; almost Kähler structure; Minkowski spacetime},
language = {eng},
number = {1-2},
pages = {99-104},
title = {Poincaré-invariant structures in the solution manifold of a nonlinear wave equation.},
url = {http://eudml.org/doc/39304},
volume = {2},
year = {1986},
}

TY - JOUR
AU - Segal, Irving E.
TI - Poincaré-invariant structures in the solution manifold of a nonlinear wave equation.
JO - Revista Matemática Iberoamericana
PY - 1986
VL - 2
IS - 1-2
SP - 99
EP - 104
AB - The solution manifold M of the equation ⎯φ + gφ3 = 0 in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on M that is Poincaré invariant. In the vanishing curvature case g = 0 the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal space-time.
LA - eng
KW - Ecuaciones diferenciales en derivadas parciales; Variedades complejas; Variedad riemanniana; nonlinear wave equation; solution manifold; Poincaré invariance; almost Kähler structure; Minkowski spacetime
UR - http://eudml.org/doc/39304
ER -