On a Moving-Frame Algorithm and the Triangulation of Equilibrium Manifolds
Werner C. Rheinboldt · Birkhäuser Basel eBooks · 1987
Nonlinear, parametrized equations 1.1 $$ \text{F}(\text{Z},\lambda ) = 0, $$ represent models of equilibrium problems for many physical systems. If F: Rn → Rm, n=m+p, p ≥ 1, is continuously differentiable on Rn, then the regular solution manifold 1.2 $$ \text M = \lbrace \text x\; \varepsilon \;\text R^{\text {n}}; \text F \left( \text x \right) =0,\; \text {rank DF} \left( \text x \right)= \text m \rbrace $$ is a p-dimensional, differentiable manifold in Rn without boundary. We shall assume always that F is at least of class Cr, r ≥ 2.