Abstract
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.
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References
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Pavlov, A. Two-dimensionalR n-gravitation. Int J Theor Phys 36, 2107–2113 (1997). https://doi.org/10.1007/BF02435947
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DOI: https://doi.org/10.1007/BF02435947