Some extensions of the class of k-convex bodies

Abstract

Abstract.1 We study relations of some classes of k-convex, k-visible bodies in Euclidean spaces. We introduce and study circular projections in normed linear spaces and classes of bodies related with families of such maps, in particular, k-circular convex and k-circular visible ones. Investigation of these bodies more general than k-convex and k-visible ones allows us to generalize some classical results of geometric tomography and find their new applications.