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 Hu, Li and Vrancken also gave a characterization of the 2-factor Calabi composition in a different manner.