Branes as solutions of gauge theories in gravitational field

The idea of the Gauss map is unified with the concept of branes as hypersurfaces embedded into $D$-dimensional Minkowski space. The map introduces new generalized coordinates of branes alternative to their world vectors $\mathbf{x}$ and identified with the gauge and other massless fields. In these coordinates the Dirac $p$-branes realize extremals of the Euler-Lagrange equations of motion of a $(p+1)$-dimensional $SO(D-p-1)$ gauge-invariant action in a gravitational backgroundComment: 21 pages. Published version: extended Introduction, additional clarifications and comments, new references and improved styl

U(1)-invariant membranes: the geometric formulation, Abel and pendulum differential equations

The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the membrane extendedness parameters. The general solution of the Abel equation is constructed. Exact solutions of the whole system of membrane equations in the D=5 Minkowski space-time are found and classified. It is shown that if the radial component of the membrane world vector is only time dependent then the dynamics is described by the pendulum equation.Comment: 19 pages, v3 published versio