Canonical form on a groupoid related to regular prolongations of Lie groups
Classical differential geometry with Christoffel symbols of Ehresmann -connections
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 -connection.
Classification des densités vectorielles factorisées
Classification of Monge-Ampère equations with two variables
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.
Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case
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.
Commuting linear operators and algebraic decompositions
For commuting linear operators we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem 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...
Completeness of the polynomial invariants of compact groups
Concomitanza, conseguenti identità di struttura e leggi di conservazione
Conformal structures associated to generic rank 2 distributions on 5-manifolds -- characterization and Killing-field decomposition.
Construction of BGG sequences for AHS structures
This paper gives a description of a method of direct construction of the BGG sequences of invariant operators on manifolds with AHS structures on the base of representation theoretical data of the Lie algebra defining the AHS structure. Several examples of the method are shown.
Contact and equivalence of submanifolds of homogeneous spaces
Contact elements on fibered manifolds
For every product preserving bundle functor on fibered manifolds, we describe the underlying functor of any order . We define the bundle of -dimensional contact elements of the order on a fibered manifold and we characterize its elements geometrically. Then we study the bundle of general contact elements of type . We also determine all natural transformations of into itself and of into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms...
Contact geometry of curves.
Continuity of liftings
Cubic forms on Riemannian surfaces
Cyclic structures of geometric objects involving a connection and Lie derivatives