Surface Motions and Fluid Dynamics

Abstract

A certain class of surface motions, including those of a relativistic membrane minimizing the 3-dimensional volume swept out in Minkowski-space, is shown to be equivalent to 3-dimensional steady-state irrotational inviscid isentropic gas-dynamics. The SU($\infty$) Nahm equations turn out to correspond to motions where the time $t$ at which the surface moves through the point $\ssatop\rhup{r}$ is a harmonic function of the three space-coordinates. This solution also implies the linearisation of a non-trivial-looking scalar field theory.

9 pages, Plain TeX, YITP/K-1069 unreadable character codes are corrected

Cited by in corpus (5)

• U(1)-invariant membranes: the geometric formulation, Abel and pendulum differential equations
• On membrane interactions and a three-dimensional analog of Riemann surfaces
• Diffeomorphism Invariant Integrable Field Theories and Hypersurface Motions in Riemannian Manifolds
• Giant graviton interactions and M2-branes ending on multiple M5-branes
• Hamiltonian Reduction of Diffeomorphism Invariant Field