Aspects of Differential Geometry V (Synthesis Lectures on Mathematics & Statistics)

Calviño-Louzao, Esteban/ García-Río, Eduardo/ Gilkey, Peter

Springer International Publishing AG（2021/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 140 p.
• 言語 ENG
• 商品コード 9783031013041

Full Description

Book V completes the discussion of the first four books by treating in some detail the analytic results in elliptic operator theory used previously. Chapters 16 and 17 provide a treatment of the techniques in Hilbert space, the Fourier transform, and elliptic operator theory necessary to establish the spectral decomposition theorem of a self-adjoint operator of Laplace type and to prove the Hodge Decomposition Theorem that was stated without proof in Book II. In Chapter 18, we treat the de Rham complex and the Dolbeault complex, and discuss spinors. In Chapter 19, we discuss complex geometry and establish the Kodaira Embedding Theorem.

Contents

Preface.- Acknowledgments.- Functional Analysis.- Elliptic Operator Theory.- Potential Theory.- Complex Geometry.- Bibliography.- Authors' Biographies.- Index.