A rigidity theorem for centroaffine Chebyshev hyperovaloids
Volume 157 / 2019
Colloquium Mathematicum 157 (2019), 133-141
MSC: Primary 53A15; Secondary 53C24, 53C42.
DOI: 10.4064/cm7382-6-2018
Published online: 15 March 2019
Abstract
In this note, we investigate centroaffine hyperovaloids. We first establish an integral formula under the additional Chebyshev condition. Then, combining the integral formula with our recent classification of locally strongly convex centroaffine hypersurfaces with parallel traceless difference tensor [J. Geom. Anal. 28 (2018), 643–655], we obtain a rigidity theorem which shows that if a centroaffine Chebyshev hyperovaloid has nonnegative centroaffine sectional curvatures then it must be an ellipsoid.
