Über die Schwerpunkte stark konvexer Bereiche der Sphäre. (About the centres of gravity of strongly convex regions of the sphere) (Q1180128)

For strictly convex subsets of the spheres \(S^ 2\) and \(S^ 3\) the author introduces quermassvectors. They are in analogy to the quermassvectors of convex bodies in Euclidean space which were studied, e.g., by the reviewer [Abh. Math. Semin. Univ. Hamb. 37, 112-132 (1972; Zbl 0229.52005)]. For these spherical quermassvectors, which after renormalization can be interpreted as curvature centroids, the author proves some properties and he derives, in particular, vector-valued Steiner formulas for the quermassvectors of outer parallel bodies.