✦ LIBER ✦

In- and circumcenters of manifolds of constant width

✍ Scribed by B. V. Dekster

Publisher: Springer
Year: 1991
Tongue: English
Weight: 193 KB
Volume: 38
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00147735

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✦ Synopsis

IN-AND CIRCUMCENTERS OF MANIFOLDS OF CONSTANT WIDTH

Bodies of constant width W in an n-dimensional Riemannian manifold M n, n t> 2, were introduced and studied in [3]. That paper dealt mostly with the curvature of the boundary of such a body K and also established that the diameter D of K satisfies D = W. Here, we deal with in-and circumcenters of K and its in-and circumradii r, and re. We prove that each circumcenter is an incenter and vice versa, establish uniqueness of such a center under certain conditions and derive the relation ri + rc = W, well known in R n. Exact definitions are as follows.

We shall assume M ~ regular but not necessarily complete. A set C c M" will be called definitely convex if

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