### 3rd order differential invariants of coframes

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Second order anti-holonomic jets as anti-symmetric parts of second order semi-holonomic jets are introduced. The anti-holonomic nature of the Lie bracket is shown. A general result on universality of the Lie bracket is proved.

We give a method based on an idea of O. Veblen which gives explicit formulas for the covariant derivatives of natural objects in terms of the Christoffel symbols of a symmetric Ehresmann $\epsilon $-connection.

This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.

This paper is a continuation of [2], dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an ‘ideal’ basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi–Ricci identities without corrections.

For commuting linear operators ${P}_{0},{P}_{1},\cdots ,{P}_{\ell}$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P={P}_{0}{P}_{1}\cdots {P}_{\ell}$ in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem $Pu=f$ reduces to a system of simpler problems. These problems capture the structure of the solution and range spaces and, if the operators involved are differential, then this gives an effective way of lowering the differential...