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On the Lie and Cartan Theory of Invariant Differential Systems, III
Antonio Kumpera
It is presently our aim to undertake the discussion, of the Parts I and II, on the infinitesimal level and outline as well the transition from infinitesimal to finite, the main rea…
On the local equivalence of partial differential equations
A. Kumpera
In all the practical applications of partial differential equations, what is mostly needed and what is in fact hardest to obtains are the solutions of the system or, occasionally,…
Group invariance of integrable Pfaffian systems
A. Kumpera
Let be an integrable Pfaffian system. If it is invariant under a transversally free infinitesimal action of a finite dimensional real Lie algebra and consequently…
Non-Integrable Pfaffian Systems
A. Kumpera
We discuss a recurrent geometrical method, due to Élie Cartan and von Weber ([1],[11]) enabling us to determine, step by step, the maximal integral manifolds of a not necessarily i…
An introduction to Lie groupoids
A. Kumpera
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-Hölder resolutions and, subseq…
On the Lie and Cartan Theory of Invariant Differential Systems, II
Antonio Kumpera
We start discussing basic properties of Lie groupoids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-Hölder resolutions and the subsequent int…
On The Equivalence Problem for Geometric Structures, II
Antonio Kumpera
This paper is a continuation of Part I where the general setup was developed. Here we discuss the general equivalence problem for geometric structures and provide criteria for the…
On The Equivalence Problem for Geometric Structures, I
Antonio Kumpera
We discuss the local and global problems for the equivalence of geometric structures of an arbitrary order and, in later sections, attention is given to what really matters, namely…