Aspects of differential geometry V [electronic resource] / Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo
- Calviño-Louzao, Esteban
- San Rafael, California (1537 Fourth Street, 1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, 
- Physical Description:
- 1 PDF (xvi, 140 pages) : illustrations (some color).
- Additional Creators:
- García-Río, Eduardo, Gilkey, Peter, Park, Jeonghyeong, and Vázquez-Lorenzo, Ramón
- Synthesis lectures on mathematics and statistics, 1938-1751 ; #41
- Restrictions on Access:
- License restrictions may limit access.
- 16. Functional analysis -- 16.1. Basic concepts in geometry and topology -- 16.2. Banach and Fréchet spaces -- 16.3. Hilbert spaces -- 16.4. Spectral theory in a separable Hilbert space, 17. Elliptic operator theory -- 17.1. Fourier transform -- 17.2. Sobolev spaces and the Rellich lemma -- 17.3. Norms on spaces of sections to a bundle -- 17.4. Spectrum of an operator of Laplace type, 18. Potential theory -- 18.1. Operators of Dirac type -- 18.2. The de Rham complex -- 18.3. Spinors -- 18.4. The Dolbeault complex -- 18.5. Duality and vanishing theorems in complex geometry, and 19. Complex geometry -- 19.1. Introduction to holomorphic geometry -- 19.2. The geometry of complex projective space -- 19.3. Hodge manifolds -- 19.4. The Kodaira embedding theorem.
- 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.
- 9781636391113 electronic, 9781636391120 hardcover, and 9781636391106 paperback
- Part of: Synthesis digital library of engineering and computer science.
- Bibliography Note:
- Includes bibliographical references (pages 129-134) and index.
- Technical Details:
- Mode of access: World Wide Web. and System requirements: Adobe Acrobat Reader.
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