Two-dimensionalR n-gravitation

A system with constraints is considered: a string theory whose Lagrangian is thenth power of the Gauss curvature of a space-time manifold (n∈N,n>1). The problem is solved exactly because after the constraints are utilized we deal with a variational problem with a trivial Lagrangian, i.e., its Euler-Lagrange equations are satisfied identically. One can say that the constraints “swallow” all dynamical degrees of freedom of the field theory. The investigation is a continuation of the 1989 work of Burlankov and Pavlov, who solved the problem of two-dimensionalR ²-gravitation under the gauge γ=1.