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General solutions of the Monge-Ampère equation in n-dimensional space |
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| Authors: | D B Fairlie A N Leznov |
| Institution: | a Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, UK b Institute for High Energy Physics, 142284 Protvino, Moscow Region, Russia |
| Abstract: | It is shown that the general solution of a homogeneous Monge-Ampère equation in n-dimensional space is closely connected with the exactly (but only implicitly) integrable system ∂ξj/∂x0 + Σk=1n−1 ξk ∂ξj/∂xk = 0 Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Ampère equation. |
| Keywords: | Monge-Ampère Gauss curvature |
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