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A Note on the Classification of Centroaffine Hypersurfaces
Abstract
Cao and Wang recently classified a class of locally strongly convex centroaffine hypersurfaces whose non-vanishing Tchebychev vector field T satisfies K(T,X)=αX and X(α)=0 for every X⊥ T, together with K(T,T)=βT. In the degenerate case β=2α, their higher-dimensional argument assumes in addition that the T⊥-component of the difference tensor K vanishes identically. We show that this extra assumption is unnecessary and the theorem can be strengthened.
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BibTeX
@misc{szancer2026note,
title = {{A Note on the Classification of Centroaffine Hypersurfaces}},
author = {Zuzanna Szancer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36095},
eprint = {2609.36095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36095},
}
RIS
TY - UNPB
TI - A Note on the Classification of Centroaffine Hypersurfaces
AU - Zuzanna Szancer
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36095
UR - https://arxiv.org/abs/2609.36095
AB - Cao and Wang recently classified a class of locally strongly convex centroaffine hypersurfaces whose non-vanishing Tchebychev vector field T satisfies K(T,X)=αX and X(α)=0 for every X⊥ T, together with K(T,T)=βT. In the degenerate case β=2α, their higher-dimensional argument assumes in addition that the T^⊥-component of the difference tensor K vanishes identically. We show that this extra assumption is unnecessary and the theorem can be strengthened.
ER -