Differentialgeometrische Methoden in der Polytoptheorie

The purpose of this thesis is to study classical objects, such as polytopes, polytopal complexes, and subspace arrangements. We will tackle problems, old and new, concerning them. We do so by using some of the new tools that have been developed in combinatorial topology, especially those tools developed in connection with (discrete) differential geometry, geometric group theory and low-dimensional topology.In dieser Arbeit werden Methoden der metrischen Geometrie, der Differentialgeometrie und der kombinatorischen Topologie benutzt um klassische Probleme in der Theorie der Polytope, der Theorie der polytopalen Komplexe und der Theorie der Unterraumarrangements zu lösen