Width and breadth for convex bodies in Riemannian manifolds (Q803940)

Bodies of constant width W in a Riemannian manifold \(M^ n\) were considered recently in a few papers. The width itself was not introduced there. The bodies were defined by means of the property that each longest geodesic within such a body orthogonal to its boundary at one of its ends has the same length W. Here, we define a width of a convex body in \(M^ n\) and show that the body is of constant width if and only if this newly introduced width is constant.