A new characterization of Calabi composition of hyperbolic affine   hyperspheres
  In this paper, we mainly prove a theorem with a corollary establishing two characterizations of the Calabi composition of hyperbolic hyperspheres, where the second characterization (i.e., the corollary) has been given via a dual correspondence theorem earlier but now we would like to use a very direct method. Note that Z.J. Hu, H.Z. Li and L. Vrancken also gave a characterization of the $2$-factor Calabi composition in a different manner. 
Xingxiao Li
math.DG