Abstract
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.
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Acknowledgements
The first two authors were supported by National Natural Science Foundation of China (Grant No. 11771404). The third author is a postdoctoral fellow of FWO-Flanders, Belgium.
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Cheng, X., Hu, Z., Moruz, M. et al. On product affine hyperspheres in ℝn+1. Sci. China Math. 63, 2055–2078 (2020). https://doi.org/10.1007/s11425-018-9457-9
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DOI: https://doi.org/10.1007/s11425-018-9457-9
Keywords
- affine hypersurface
- affine metric
- affine hypersphere
- Levi-Civita connection
- constant sectional curvature
- parallel Ricci tensor