Centroaffine geometry of equiaffine rotation surfaces in R3R3

We study the invariant properties for affine rotation surfaces in 3-affine space R3R3 under the centroaffine transformation group. With the additional property of the vanishing centroaffine Pick invariant, a complete classification is obtained. By solving certain differential equations, we also give some classification results for centroaffine minimal rotation surfaces with the constant tensor norm of the Tchebychev vector field induced by the centroaffine metric.