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Journal Articles Pacific Journal of Mathematics Year : 2021

Affine hypersurfaces with constant sectional curvature

Miroslava Antić
  • Function : Author
Haizhong Li
  • Function : Author
Xianfeng Wang
  • Function : Author

Abstract

We use a new approach to study locally strongly convex hypersurfaces with constant sectional curvature in the affine space (Formula presented). We prove a nice relation involving the eigenvalues of the shape operator S and the difference tensor K of the affine hypersurface. This is achieved by making full use of the Codazzi equations for both the shape operator and the difference tensor and the Ricci identity in an indirect way. Starting from this relation, we give a classification of locally strongly convex hypersurface with constant sectional curvature whose shape operator S has at most one eigenvalue of multiplicity one.
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Dates and versions

hal-03722534 , version 1 (13-07-2022)

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Miroslava Antić, Haizhong Li, Luc Vrancken, Xianfeng Wang. Affine hypersurfaces with constant sectional curvature. Pacific Journal of Mathematics, 2021, 310 (2), pp.275-302. ⟨10.2140/pjm.2021.310.275⟩. ⟨hal-03722534⟩
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