ebook9783110905434d4325

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For most mathematicians and many mathematical physicists the name Erich K√§hler is strongly tied to important geometric notions such as K√§hler metrics, K√§hler manifolds and K√§hler groups. They all go back to a paper of 14 pages written in 1932. This, however, is just a small part of K√§hler’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 Dieudonn√©. 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 K√§hler’s mathematical papers are collected following a “Tribute to Herrn Erich K√§hler” by S. S. Chern, an overview of K√§hler’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 K√§hler’s work, starting by W. Neumann’s paper on the topology of hypersurface singularities, J.-P. Bourguignon’s report on K√§hler geometry and, among others by Berndt, Bost, Deitmar, Ekeland, Kunz and Krieg, up to A. Nicolai’s essay “Supersymmetry, K√§hler geometry and Beyond”. As K√§hler’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 “Approach to the philosophy of Erich K√§hler”.