Gravitation theory generated by dimensional continuation of the Euler characteristic as a constrained Hamiltonian system

The authors study the Hamiltonian formulation of the most general gravitation theory in d spacetime dimensions which has only the spatial metric and its conjugate momentum as canonical variables. The action of that theory is generated by dimensional continuation of the Euler characteristics associated to all the lower even dimensions. The constraint-generators are worked out. The expression for the velocities in terms of the momenta cannot be given in closed form since it involves the solution of a system of non linear algebraic equations. This leads to a Hamiltonian which is multivalued at high curvatures. The boundary term which must be added to the dimensionally continued Euler characteristic in order to eliminate the second time derivatives is always proportional to the trace of the conjugate momentum