Flat centroaffine surfaces with the degenerate second fundamental form and vanishing Pick invariant in R4

In this paper, we get the centroaffine theorema egregium of centroaffine immersions with codimension two. Then by solving certain partial differential equations, we obtain some classification results for flat centroaffine surfaces in R4, under the condition of degenerate second fundamental form and vanishing Pick invariant. Finally, some examples with respect to the classification results are discussed.