Centroaffine ruled surfaces in \(\mathbb R^3\) (Q2267488)

The authors consider non-degenerate ruled surfaces \(x:M^2\to\mathbb{R}^3\), where \(M^2\) is a 2-dimensional parameter manifold with transversal position vector. \(x\) has a representation \(x(u,v)= a(u)+ v\cdot b(u)\) with parameters \(u\), \(v\) and \(a(u), b(u)\in\mathbb{R}^3\). The authors prove classification results under additional assumptions for centroaffine invariants. Reviewer's remarks: {\parindent7mm \begin{itemize}\item[(i)] The variational problem for the centroaffine area functional leads to the Euler-Lagrange equation trace \({\mathfrak T}= 0\), where \({\mathfrak T}\) is the so-called centroaffine Tchebychev operator. \({\mathfrak T}\) gives no information on `extrinsic curvature', thus the notion ``centroaffine mean curvature''' for trace \({\mathfrak T}\) might be misleading in the reviewer's opinion. \item[(ii)] The publisher of the journal should make sure that the English of an article is corrected before publication. \end{itemize}}