An introduction to the theory of generalized conics and their applications
Let \(\Gamma\) be a fixed point set in a Euclidean space. A generalized conic is a set of points with the same average distance from \(\Gamma\). In this paper, the authors give a process to construct convex bodies which are invariant under a fixed subgroup of the orthogonal group in the Euclidean space, using generalized conics. As an application, the authors consider the holonomy group of Riemannian manifolds and prove some metrizable results. In particular, they prove that there are eight classes of manifolds equipped with an invariant smooth collection of Minkowski functionals on the tangent spaces, called Berwalds spaces in a general sense.
scientific article; zbMATH DE number 5865473
scientific article