From Riemann Manifolds to Riemann Manifolds - Map Projections: Cartographic Information Systems - page 49

Fig. 1.22. Lichtenstein, L.: Zur Theorie der konformen Abbildung. Konforme Abbildung nichtanalytischer sin-
gularitatenfreier Flachenstucke auf ebene Gebiete (Bull. Int. Acad. Sci. Cracovie, Chasse des Sciences, Math. et
Natur., Serie A, pp. 192-217, Cracovie 1916). Part one
We shall define conformeophism as well as angular shear, and shall present the equivalence theorem
that relates conformeomorphism to a special structure of the Cauchy-Green deformation tensor,
the Euler-Lagrange deformation tensor, the left and right principal stretches (left and right eigen-
values) as well as dilatations, before we are led to the generalized Korn-Lichtenstein equations
which govern any conformal mapping: compare with Definition 1.10 and Theorem 1.11 .Fora
further motivation, we refer to Fig. 1.22 and Fig. 1.23 , which presents an image of Lichtenstein's
original publication “Zur Theorie der konformen Abbildung”.