On equivalence of vector-valued maps

TL;DR

This paper presents a new approach to determine when vector-valued maps are equivalent, applicable to paths and patches in differential geometry, without requiring smoothness for certain cases.

Contribution

It introduces a general method for the equivalence problem of vector-valued maps, extending to paths and patches without smoothness assumptions.

Findings

Provides a unified framework for equivalence of vector-valued maps

Applies to differential geometry paths and patches

Does not require smoothness in certain cases

Abstract

An approach to the equivalence problem of vector valued maps is offered which, in particular, covers the equivalence problem of paths and patches of differential geometry with respect to different motion groups. In the last case, in contrary to differential geometry case, it does not need and does not use smoothness of paths and patches to get the corresponding main results.