By Werner Ballmann
Those notes are in line with lectures the writer gave on the collage of Bonn and the Erwin Schrödinger Institute in Vienna. the purpose is to offer a radical creation to the idea of Kähler manifolds with distinctive emphasis at the differential geometric facet of Kähler geometry. The exposition begins with a quick dialogue of advanced manifolds and holomorphic vector bundles and an in depth account of the fundamental differential geometric houses of Kähler manifolds. The extra complicated subject matters are the cohomology of Kähler manifolds, Calabi conjecture, Gromov's Kähler hyperbolic areas, and the Kodaira embedding theorem. a few familiarity with international research and partial differential equations is thought, specifically within the half at the Calabi conjecture. There are appendices on Chern-Weil conception, symmetric areas, and $L^2$-cohomology.
A ebook of the eu Mathematical Society (EMS). dispensed in the Americas by way of the yank Mathematical Society.
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