A rigidity theorem for centroaffine Chebyshev hyperovaloids
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.