W.Quapp, O.Imig, D.Heidrich:

in: The Reaction Path in Chemistry, (Ed.: D.Heidrich), 
Kluwer Academic Press, Dordrecht, 1995, p.137-160. 

"Gradient extremals and their relation to the minimum energy path" 

The problem of defining (and tracing) a chemically
meaningful reaction path (RP) of potential 
energy surfaces (PES) is reinvestigated in the light of the so called
gradient extremal (GE). GE of n-dimensional hypersurfaces, 
E=E(x^1,...,x^n),  are curves defined by the condition that the
gradient, nabla E, is an eigenvector of the Hessian matrix,
nabla nabla E. 
The relationship between the conventional steepest descent path (SDP)
and GE is discussed using the curvature of SDP.
A classification of the solutions of the
gradient extremal equation is given for the two-dimensional case.   
GE following is considered as a tool to detect the true valley paths
explained by instructive model surfaces. Singular points on 
the PES, where valleys or ridges emerge, dissipate, or bifurcate, are
included in the analysis. 
To the end, a discussion is given to a third, new possibility to  
describe a true valley floor line by pure curvature extrema of the
level lines.