This book is a collection of mathematical papers written by Erich Kähler, together with almost 200 pages of commentaries on his mathematical work and an appendix with three of his philosophical papers. The book begins with a short description of his life (by R. Berndt and A. Bohm) and a survey of his contribution to mathematics (by R. Berndt and O. Riemenschneider). In the second part of the book, 32 of Kähler’s mathematical articles are reproduced. The third part offers commentaries on the mathematical work of Kähler covering the main parts of his research. It includes papers by W. D. Neumann (Topology of hypersurface singularities), J.-P.Bouguignon (The unabated vitality of Kähler geometry), H. Nicolai (Supersymmetry, Kähler geometry and beyond) and I. Eceland (Some applications of the Cartan-Kähler theorem to economic theory). Comments on the philosophical work of Kähler are written by R. Berndt and K. Maurin. E. Kähler was a mathematician of broad interests and his influence is clearly visible in many fields of mathematics and mathematical physics (e.g. notions of Kähler and Einstein-Kähler metrics, Kähler and hyper-Kähler manifolds and Kähler groups). The book offers a summary of his work and makes it more accessible to contemporary readers.

Reviewer:

jbu