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The decomposition of global conformal invariants [electronic resource] /
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| 자료유형 | E-Book |
|---|---|
| 개인저자 | Alexakis, Spyros, 1978- |
| 서명/저자사항 | The decomposition of global conformal invariants[electronic resource] /Spyros Alexakis. |
| 발행사항 | Princeton : Princeton University Press, 2012. |
| 형태사항 | 1 online resource (460 p.) |
| 총서사항 | Annals of mathematics studies ;no. 182 |
| ISBN | 9781400842728 (electronic bk.) 1400842727 (electronic bk.) |
| 내용주기 | Cover Page; Title Page; Copyright Page; Table of Contents; Acknowledgments; 1. Introduction; 1.1 Related Questions; 1.2 Outline of this Work; 2. An Iterative Decomposition of Global Conformal Invariants: The First Step; 2.1 Introduction; 2.2 Conventions, Background, and the Super Divergence Formula; 2.3 From the super Divergence Formula for Ig(첩) Back to P(g): The Two Main Claims of this Work; 2.4 Proposition 2.7 in the Easy Case s = s; 2.5 Proposition 2.7 in the Hard Case s <s; 3. The Second Step: The Fefferman-Graham Ambient Metric and the Nature of the Decomposition; 3.1 Introduction. 3.2 The Locally Conformally Invariant Piece in P(g): A Proof of Lemmas 3.1, 3.2, and 3.33.3 Proof of Lemma 3.4: The Divergence Piece in P(g); 4. A Result on the Structure of Local Riemannian Invariants: The Fundamental Proposition; 4.1 Introduction; 4.2 The fundamental Proposition 4.13; 4.3 Proof of Proposition 4.13: Set up an Induction and Reduce the Inductive Step to Lemmas 4.16, 4.19, 4.24; 4.4 Proof that Proposition 4.13 Follows from Lemmas 4.16, 4.19, and 4.24 (and Lemmas 4.22 and 4.23); 5. The Inductive Step of the Fundamental Proposition: The Simpler Cases; 5.1 Introduction. 5.2 Notation and Preliminary Results5.3 An analysis of Curvtrans[Lg]; 5.4 A study of LC[Lg] and W[Lg] in (5.16): Computations and cancellations; 6. The Inductive Step of the Fundamental Proposition: The Hard Cases, Part I; 6.1 Introduction; 6.2 The First Ingredient in the Grand Conclusion; 6.3 The Second Part of the Grand Conclusion: A study of Image 1,횩 횠u+1 [Lg]=0; 6.4 The Grand Conclusion and the Proof of Lemma 4.24; 7. The Inductive Step of the Fundamental Proposition: The Hard Cases, Part II; 7.1 Introduction: A sketch of the Strategy; 7.2 The proof of Lemma 4.24 in Case B; A. Appendix. A.1 Some Technical ToolsA. 2 Some Postponed Short Proofs; A.3 Proof of Lemmas 4.22 and 4.23; Bibliography; Index of Authors and Terms; Index of Symbols. |
| 요약 | This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Deser. |
| 일반주제명 | Conformal invariants. Decomposition (Mathematics) Mathematics. MATHEMATICS / Numerical Analysis. MATHEMATICS / Geometry / Differential. |
| 언어 | 영어 |
| 기타형태 저록 | Print version:Alexakis, Spyros.Decomposition of Global Conformal Invariants (AM-182).Princeton : Princeton University Press, 20129780691153476 |
| 대출바로가기 | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=439689 |
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| No. | 등록번호 | 청구기호 | 소장처 | 도서상태 | 반납예정일 | 예약 | 서비스 | 매체정보 |
|---|---|---|---|---|---|---|---|---|
| 1 | WE00002728 | 518 | 가야대학교/전자책서버(컴퓨터서버)/ | 대출가능 |
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