Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Antonio Kumpera
Pages: [1] - [71]
Received Date: May 30, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121508
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, the equivalence with respect to transformations belonging to a given pseudo-group of transformations. We first give attention to general prolongation spaces and thereafter insert the structures in their most appropriate ambient, namely, as specific solutions of partial differential equations, where the equivalence problem is then discussed. In the second part, we discuss applications of all this abstract nonsense and take considerable advantage in exploring Élie Cartan’s magical trump called transformations et prolongements mériédriques that somehow seem absent in present day geometry.
prolongation spaces, structures equivalence, differential invariants.
