Bücher von Erich Kahler

Erich Kahler sees cultural history as a subtle process in which reality plays upon consciousness and consciousness itself is forever transforming reality. He traces the ebb and flow of this relationship by studying changes in narrative form from its beginnings in the Gilgamesh Cycle to the end of the eighteenth century. The general direction is toward a growing inwardness, he finds; what takes place is an expansion of consciousness as man constantly draws outer space, the contents of a more and more complex world, into what Rilke called Weltinnenraum, "e;inner space."e;Originally published in 1973.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

For most mathematicians and many mathematical physicists the name Erich Kahler is strongly tied to important geometric notions such as Kahler metrics, Kahler manifolds and Kahler groups. They all go back to a paper of 14 pages written in 1932. This, however, is just a small part of Kahler's many outstanding achievements which cover an unusually wide area: From celestial mechanics he got into complex function theory, differential equations, analytic and complex geometry with differential forms, and then into his main topic, i.e. arithmetic geometry where he constructed a system of notions which is a precursor and, in large parts, equivalent to the now used system of Grothendieck and Dieudonne. His principal interest was in finding the unity in the variety of mathematical themes and establishing thus mathematics as a universal language. In this volume Kahler's mathematical papers are collected following a "e;Tribute to Herrn Erich Kahler"e; by S. S. Chern, an overview of Kahler's life data by A. Bohm and R. Berndt, and a Survey of his Mathematical Work by the editors. There are also comments and reports on the developments of the main topics of Kahler's work, starting by W. Neumann's paper on the topology of hypersurface singularities, J.-P. Bourguignon's report on Kahler geometry and, among others by Berndt, Bost, Deitmar, Ekeland, Kunz and Krieg, up to A. Nicolai's essay "e;Supersymmetry, Kahler geometry and Beyond"e;. As Kahler's interest went beyond the realm of mathematics and mathematical physics, any picture of his work would be incomplete without touching his work reaching into other regions. So a short appendix reproduces three of his articles concerning his vision of mathematics as a universal Theme together with an essay by K. Maurin giving an "e;Approach to the philosophy of Erich Kahler"e;.