Convex bodies all whose sections (projections) are equal

Abstract

Introduction 1 2. Aleksandrov's theorem 2 3. Congruent and similar sections 3 3.1. Fields of convex bodies 3 3.2. The proof of Schneider's theorem and similar sections 5 4. Affinely equivalent sections and the Banach conjecture 5 4.1. The Banach conjecture 6 4.2. Topology of Lie groups 6 4.3. The case n = 5 8 4.4. Affine bodies of revolution 10 4.5. The Banach Conjecture, when n is odd and dim V ≥ n + 2 13 4.6. The complex Banach conjecture 15 5. Convex bodies all whose orthogonal projections are equal 17 5.1. Equal area, congruence and affine equivalence 17 5.2. The codimension 2 case for orthogonal projections 18 References 20