Skip to Main content Skip to Navigation
Journal articles

Affine hypersurfaces with constant sectional curvature

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.
Document type :
Journal articles
Complete list of metadata

https://hal-uphf.archives-ouvertes.fr/hal-03722534
Contributor : Kathleen TORCK Connect in order to contact the contributor
Submitted on : Wednesday, July 13, 2022 - 2:32:01 PM
Last modification on : Thursday, July 14, 2022 - 3:55:32 AM

Identifiers

Collections

Citation

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

Share

Metrics

Record views

5