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On product affine hyperspheres in ℝn+1

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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https://hal-uphf.archives-ouvertes.fr/hal-03722937
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Submitted on : Wednesday, July 13, 2022 - 5:19:49 PM
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Xiuxiu Cheng, Zejun Hu, Marilena Moruz, Luc Vrancken. On product affine hyperspheres in ℝn+1. Science China Mathematics, Science China Press, 2020, 63 (10), pp.2055-2078. ⟨10.1007/s11425-018-9457-9⟩. ⟨hal-03722937⟩

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