On The Equivalence Problem for Geometric Structures, I

2014/12/29 by Antonio Kumpera, Kumpera, Antonio
Computer Science · Engineering · #53C17 #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C05 #Secondary 53C15

paper · pdf · doi:10.48550/arxiv.1412.8391

openalex publication_date 2014/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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