An analogue of the Sauer theorem.
The theorem of \textit{R. Sauer} [Math. Ann. 111, 71--82 (1935; Zbl 0010.37402, JFM 61.0744.04)] asserts that between bending fields of two projectively equivalent surfaces in Euclidean space \(E^3\) a bijection can be established so that to the trivial shift fields of one surface correspond the trivial shift fields of the other surface. Here, an analogue is proven for simply connected surfaces \(F^2:{\mathbf r}={\mathbf r}(u, v)\), \((u,v)\in D\) of class \(C^2(D)\) in \(E^3\), where bending fields are replaced by infinitely small equi-areal deformations and bijection preserves the pointwise spherical map (i.e. for which the variation \(\delta{\mathbf n}\) of a normal unit vector field \({\mathbf n}\) is collinear to \({\mathbf n}\)).
scientific article; zbMATH DE number 2121055