When a spherical body of constant diameter is of constant width?

Abstract

{\bf Abstract.} Let $D$ be a convex body of diameter $\delta$, where $0<\delta <\frac{\pi }{2}$, on the $d$-dimensional sphere. We prove that $D$ is of constant diameter $\delta$ if and only if it is of constant width $\delta$ in the following two cases. The first case is when $D$ is smooth. The second case is when $d=2$.

7 pages, 2 figures

References in corpus (1)

• On the works of Euler and his followers on spherical geometry