Laplace-Beltrami operator and exact solutions for branes

Abstract

Proposed is a new approach to finding exact solutions of nonlinear $p$-brane equations in $D$-dimensional Minkowski space based on the use of various initial value constraints. It is shown that the constraints ${\Delta }^{(p)}\vec{x}=0$ and ${\Delta }^{(p)}\vec{x}=-\Lambda (t,{\sigma }^r)\vec{x}$ give two sets of exact solutions.

22 pages, v2: Section on folded p-branes and refs added; typos corrected; minor corrections. To appear in Nucl. Phys. B

References in corpus (4)

• Exact solutions for U(1) globally invariant membranes
• U(1)-invariant membranes: the geometric formulation, Abel and pendulum differential equations
• Toroidal p-branes, anharmonic oscillators and (hyper)elliptic solutions
• Extended Particles and the Exterior Calculus

Cited by in corpus (2)

• $p$-Branes with $Ad{S}_{p+1}$ vacuum as models of $R^2$ gravity
• Branes as solutions of gauge theories in gravitational field