Nonholonomic geometry of economic systems

The paper connects the Vr˘anceanu congruence theory with Udris¸te theory of odd-dimensional nonholo- nomic economic systems. To build an orthonormalization Riemannian metric, the authors use certain congruences with economic meaning. Based on this metric, the authors build the differential invariants of the nonholonomic economic space in terms of Vr˘anceanu-Riemann. Further, one proves that the coefficients of bilinear covariants and the coefficients of Ricci (with three and four indexes) are signomials, and the tangent vectors to the geodesics are rational functions of some economic potentials. As novelty, one introduces and studies also the submanifold of coefficients of bilinear covariants, the submanifold of Ricci rotation coefficients and the submanifold of Ricci coefficients with four indexes.