Selected Papers of Wilhelm P.A. Klingenberg (Series in Pure Mathematics)

This work is an introduction to module theory for the reader who knows something about linear algebra and ring theory. The main aim of the book is the derivation of the structure theory of modules over Euclidean domains. This theory is applied to obtain the structure of abelian groups and the rational canonical and Jordan normal forms of matrices. The basic facts about rings and modules are given in full generality so that some further topics can be discussed, including projective modules, and the connection between modules and representation of groups. The book is intended to serve as supplementary reading for the third or fourth year undergraduate who is taking a course in module theory "This set of selected papers of Klingenberg covers some of the important mathematical aspects of Riemannian Geometry, Closed Geodesics, Geometric Algebra, Classical Differential Geometry and Foundations of Geometry of Klingenberg. Of significance were his contributions to Riemannian Geometry in the Large which opened a new area in Global Riemannian Geometry. He also introduced the Hilbert manifold of closed curves of class H1 on a Riemannian manifold. In connection with his work in closed geodesics, he became interested in the properties of the geodesic flow. Classical results from dynamical systems became useful tools for the study of closed geodesics. He was also credited for drawing closer together Riemannian Geometry and Hamiltonian systems, which had developed separately since the time of H Poincaré. Besides publishing research papers, Klingenberg also wrote a dozen books and lecture notes, among which is the important reference work "Riemannsche Geometrie im Groβen"." I was born on January 28, 1924 in Rostock, the oldest child of a Protestant minister, Paul Klingenberg, and his wife Henny Dunker.