Centroaffine differential geometry and its relations to horizontal submanifolds
Volume 57 / 2002
Banach Center Publications 57 (2002), 21-28
MSC: Primary 53A15
DOI: 10.4064/bc57-0-3
Abstract
We relate centroaffine immersions $f: M^n \rightarrow {\mathbb{R}}^{n+1}$ to horizontal immersions $g$ of $M^n$ into $S^{2n+1}_{n+1}(1)$ or $H^{2n+1}_n(-1)$. We also show that $f$ is an equiaffine sphere, i.e. the centroaffine normal is a constant multiple of the Blaschke normal, if and only if $g$ is minimal.
