Cartesian coordinates Differential geometry

Additionally, questions of the coordinate invariance of these paths have to be answered (cf. Refs. 24a,25a,9a and Chap.3). Starting with the Cartesian coordinate system, one may transform and describe the RP in any other coordinate systems by means of differential geometry. In this manner, a gradient path (e.g. the steepest descent) is invariant with respect to the choice of the coordinate system and may be regarded as a fundamental (mathematical) characteristic of a chemical reaction. 

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