W.Quapp:
in: 
The Reaction Path in Chemistry, (Ed.: D.Heidrich),
 
Kluwer Academic Press, Dordrecht, 1995, p.95-108.

"The invariance of reaction paths description in any coordinate system" 

Reaction paths are a widely used concept of theoretical chemistry. It
seems that the invariance problem, which was mathematically solved a   
long time ago, does again and again penetrate all periods of discussion
of this field of theory 
[see: J. Chem. Soc. Faraday Disc. 90,No.12, 1994]. 
We give the non-invariant, and the invariant
definitions of two kinds of chemical reaction paths, of the steepest
descent lines, and of gradient extremal curves, respectively the choice
of the coordinate system for the description of the potential energy   
surface and the reaction path valley.