On starshaped sets. (English) Zbl 0689.53006

Beltagy, M.

Bull. Malays. Math. Soc., II. Ser. 11, No. 2, 49-57 (1988).

The author points out that certain theorems on star-shaped sets in Euclidean space may be seen, by using the projective model of hyperbolic space, to have exact analogues in hyperbolic space \(H^ n\). For instance, a compact immersed hypersurface of \(H^ n\) whose tangent totally geodesic hyperplanes do not fill up \(H^ n\) is imbedded as the boundary of a star-shaped body, as follows from the corresponding Euclidean theorem of B. Halpern [Proc. Am. Math. Soc. 30, 181-184 (1971; Zbl 0222.57016)].

Reviewer: S.Alexander

MSC:

53A35

Non-Euclidean differential geometry

Keywords:

hyperbolic space; star-shaped body

Citations:

Zbl 0222.57016