- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:41
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
2
1986
1
Poincaré-Invariant Structures in the Solution Manifold of a Nonlinear Wave Equation
Irving
Segal
Massachusetts Institute of Technology, CAMBRIDGE, UNITED STATES
The solution manifold $M$ of the equation $\phi + g\phi^3 = 0$ 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.
General
99
104
10.4171/RMI/28
http://www.ems-ph.org/doi/10.4171/RMI/28