Mathematische Werke

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Erich Kähler is renowned among mathematicians and mathematical physicists for his contributions to geometric concepts like Kähler metrics, manifolds, and groups, all stemming from a pivotal 1932 paper. However, his achievements extend far beyond this, encompassing a broad spectrum of fields. He transitioned from celestial mechanics to complex function theory, differential equations, and analytic geometry, ultimately focusing on arithmetic geometry. Here, he developed a framework that parallels the systems later established by Grothendieck and Dieudonné. Kähler sought to unify diverse mathematical themes, promoting mathematics as a universal language. This volume compiles Kähler's mathematical papers, introduced by a tribute from S. S. Chern, an overview of his life by A. Bohm and R. Berndt, and a survey of his work by the editors. It includes discussions on key topics in Kähler's research, featuring contributions from W. Neumann on hypersurface singularities and J.-P. Bourguignon on Kähler geometry, among others. Additionally, the collection addresses Kähler's broader interests, with an appendix showcasing three articles that reflect his vision of mathematics as a universal theme, alongside K. Maurin's essay on Kähler's philosophy.