Abstract
Liu and Wang (Beiträge Algebra Geom 35:109–117, 1994) determined homogeneous nondegenerate centroaffine surfaces in the 3-dimensional affine space. However, n-dimensional homogeneous or locally homogeneous nondegenerate centroaffine hypersurfaces for \(n\ge 3\) have not been completely classified yet. In this paper, we determine 3-dimensional locally homogeneous nondegenerate centroaffine hypersurfaces with nondiagonalizable Tchebychev operator.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Li, A.M., Wang, C.P.: Canonical centroaffine hypersurfaces in \(R^{n+1}\). Results Math. 20, 660–681 (1991)
Liu, H.L., Wang, C.P.: Centroaffine homogeneous surfaces in \(R^3\). Beiträge Algebra Geom. 35, 109–117 (1994)
Liu, H.L., Wang, C.P.: The centroaffine Tchebychev operator. Results Math. 27, 77–92 (1995)
Nomizu, K., Sasaki, T.: Affine Differential Geometry. Cambridge University Press, Cambridge (1994)
Ooguri, M.: The classification of 3-dimensional locally homogeneous Blaschke hypersurfaces with nondiagonalizable affine shape operators. Soochow J. Math. 32, 379–398 (2006)
Ooguri, M.: Three dimensional locally homogeneous nondegenerate centroaffine hypersurfaces with null Tchebychev vector field. Beiträge Algebra Geom. (2013, to appear)
Wang, C.P.: Centroaffine minimal hypersurfaces in \(R^{n+1}\). Geom. Dedicata 51, 63–74 (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ooguri, M. Three-dimensional locally homogeneous nondegenerate centroaffine hypersurfaces with nondiagonalizable Tchebychev operator. Results Math 71, 1–14 (2017). https://doi.org/10.1007/s00025-016-0623-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-016-0623-y