2025/09/22 by Morales-Amaya, Efrén
#FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2509.17326
Let K⊂ ℝn be a convex body and let p in the interior of K, n ≥ 3. The point p is said to be a Larman point of K if, for every hyperplane Π passing through p, the section Π∩ K has a (n-2)-plane of symmetry. If, in addition, for every hyperplane Π passing through p, the section Π∩ K has a (n-2)-plane of symmetry which contains p, then the point p is called a revolution point. In this work we prove that if for the convex body K, n ≥ 3, there exists a hyperplane H, a point p such that p is a Larman point of K but not a revolution point and, for every hyperplane Π passing though p, the section Π∩ K has an (n-2)-plane of symmetry parallel to H, then K is an ellipsoid of revolution with an axis perpendicular to H.