On product affine hyperspheres in $\mathbb{R}^{n+1}$
Differential Geometry
2021-02-03 v1
Abstract
In this paper, we study locally strongly convex affine hyperspheres in the unimodular affine space which, as Riemannian manifolds, are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional curvatures. As the main result, a complete classification of such affine hyperspheres is established. Moreover, as direct consequences, affine hyperspheres of dimensions 3 and 4 with parallel Ricci tensor are also classified.
Keywords
Cite
@article{arxiv.1812.07901,
title = {On product affine hyperspheres in $\mathbb{R}^{n+1}$},
author = {Xiuxiu Cheng and Zejun Hu and Marilena Moruz and Luc Vrancken},
journal= {arXiv preprint arXiv:1812.07901},
year = {2021}
}
Comments
27 pages. This article has been accepted for publication in SCIENCE CHINA Mathematics