In this paper,we study locally strongly convex affine hyperspheres in the unimodular affine space Rn+1 which,as Riemannian manifolds,are locally isometric to the Riemannian product of two Riemannian manifolds both pos...In this paper,we study locally strongly convex affine hyperspheres in the unimodular affine space Rn+1 which,as Riemannian manifolds,are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional curvature.As the main result,a complete classification of such affine hyperspheres is established.Moreover,as direct consequences,3-and 4-dimensional affine hyperspheres with parallel Ricci tensor are also classified.展开更多
In this paper, continuing with Hu-Li Vrancken and the recent work of Antid Dillen- Schoels-Vrancken, we obtain a decomposition theorem which settled the problem of how to determine whether a given locally strongly con...In this paper, continuing with Hu-Li Vrancken and the recent work of Antid Dillen- Schoels-Vrancken, we obtain a decomposition theorem which settled the problem of how to determine whether a given locally strongly convex aitine 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.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11771404)。
文摘In this paper,we study locally strongly convex affine hyperspheres in the unimodular affine space Rn+1 which,as Riemannian manifolds,are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional curvature.As the main result,a complete classification of such affine hyperspheres is established.Moreover,as direct consequences,3-and 4-dimensional affine hyperspheres with parallel Ricci tensor are also classified.
基金supported by the Ministry of Science and Technological Development of Serbia,Pro ject174012supported by NSFC(Grant No.11371330)supported by NSFC(Grant Nos.11326072 and 11401173)
文摘In this paper, continuing with Hu-Li Vrancken and the recent work of Antid Dillen- Schoels-Vrancken, we obtain a decomposition theorem which settled the problem of how to determine whether a given locally strongly convex aitine 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.
