Geometry of simplices in Minkowski spaces

摘要

There are many problems and configurations in Euclidean geometry that werenever extended to the framework of (normed or) finite dimensional real Banachspaces, although their original versions are inspiring for this type ofgeneralization, and the analogous definitions for normed spaces represent apromising topic. An example is the geometry of simplices in non-Euclideannormed spaces. We present new generalizations of well known properties ofEuclidean simplices. These results refer to analogues of circumcenters, Eulerlines, and Feuerbach spheres of simplices in normed spaces. Using duality, wealso get natural theorems on angular bisectors as well as in- and exspheres of(dual) simplices.