Characterization of the generalized Calabi composition of affine hyperspheres

M. Antic , Z. Hu , C. C. Li , Luc Vrancken (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

In this paper, continuing with Hu-Li-Vrancken and the recent work of Antie-Dillen-Schoels Vrancken, we obtain a decomposition theorem which settled the problem of how to determine whether a given locally strongly convex affine hypersurface can be decomposed as a generalized Calabi composition of two affine hyperspheres, based on the properties of its difference tensor K and its affine shape operator S.

Domaines: Mathématiques [math]

M. Antic, Z. Hu, C. C. Li, Luc Vrancken. Characterization of the generalized Calabi composition of affine hyperspheres. Acta Mathematicae Applicatae Sinica, 2015, 31 (10), pp.1531-1554. ⟨10.1007/s10114-015-4431-1⟩. ⟨hal-03233620⟩