Convex Bodies with affinely equivalent projections and affine bodies of revolution

2020/05/05 by Luis Montejano, Montejano, Luis
Mathematics · #22E10 #52A05 #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2005.02290

openalex publication_date 2020/05/05 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28

Abstract

Abstract In this paper, we study affine bodies of revolution. This will allow us to prove that a convex body all whose orthogonal n-projections are affinely equivalent is an ellipsoid, provided n≡ 0,1, 2 mod 4, n>1 with the possible exemption of n=133. Our proof uses convex geometry and topology of compact Lie groups. AMS classification subject: 22E10, 52A05

Related

• John Ellipsoids of Revolution
• The extremal volume ellipsoids of convex bodies, their symmetry properties, and their determination in some special cases
• Characterizations of symmetric convex sets
• Shadows of convex bodies
• Regular ellipsoids and a Blaschke-Santaló-type inequality for projections of non-symmetric convex bodies