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Kanonische Metriken in Kähler Geometrie von Gang Tian: Neu-
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eBay-Artikelnr.:286137250316
Artikelmerkmale
- Artikelzustand
- Book Title
- Canonical Metrics in Kähler Geometry
- Publication Date
- 2000-08-01
- Pages
- 101
- ISBN
- 9783764361945
Über dieses Produkt
Product Identifiers
Publisher
Springer Basel A&G
ISBN-10
3764361948
ISBN-13
9783764361945
eBay Product ID (ePID)
1668036
Product Key Features
Number of Pages
VII, 101 Pages
Language
English
Publication Name
Canonical Metrics in Kähler Geometry
Publication Year
2000
Subject
Geometry / Differential, Geometry / General, Poetry, Physics / Mathematical & Computational, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics, Literary Criticism, Science
Series
Lectures in Mathematics. Eth Zürich Ser.
Format
Trade Paperback
Dimensions
Item Height
0.1 in
Item Weight
16.2 Oz
Item Length
10 in
Item Width
7 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
99-038968
Dewey Edition
21
Notes by
Akveld, M.
Reviews
"This little monograph offers an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds. …The author presents some advanced topics which are hard [to] find elsewhere… This graduate course on Kähler-Einstein metrics can be recommended to all those interested in recent developments within complex differential geometry." --Publicationes Mathematicae "This monograph includes an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds." --Zentralblatt Math, "This little monograph offers an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds. …The author presents some advanced topics which are hard [to] find elsewhere… This graduate course on Kähler-Einstein metrics can be recommended to all those interested in recent developments within complex differential geometry."--Publicationes Mathematicae"This monograph includes an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds."--Zentralblatt Math, "This little monograph offers an essentially self-contained introduction to the theory of canonical Khler metrics on complex manifolds. ...The author presents some advanced topics which are hard [to] find elsewhere... This graduate course on Khler-Einstein metrics can be recommended to all those interested in recent developments within complex differential geometry." --Publicationes Mathematicae "This monograph includes an essentially self-contained introduction to the theory of canonical Khler metrics on complex manifolds." --Zentralblatt Math, "This little monograph offers an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds. ...The author presents some advanced topics which are hard [to] find elsewhere... This graduate course on Kähler-Einstein metrics can be recommended to all those interested in recent developments within complex differential geometry." --Publicationes Mathematicae "This monograph includes an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds." --Zentralblatt Math
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515/.73
Table Of Content
1 Introduction to Kähler manifolds.- 1.1 Kähler metrics.- 1.2 Curvature of Kähler metrics.- 2 Extremal Kähler metrics.- 2.1 The space of Kähler metrics.- 2.2 A brief review of Chern classes.- 2.3 Uniformization of Kähler-Einstein manifolds.- 3 Calabi-Futaki invariants.- 3.1 Definition of Calabi-Futaki invariants.- 3.2 Localization formula for Calabi-Futaki invariants.- 4 Scalar curvature as a moment map.- 5 Kähler-Einstein metrics with non-positive scalar curvature.- 5.1 The Calabi-Yau Theorem.- 5.2 Kähler-Einstein metrics for manifolds with c1(M) < 0.- 6 Kähler-Einstein metrics with positive scalar curvature.- 6.1 A variational approach.- 6.2 Existence of Kähler-Einstein metrics.- 6.3 Examples.- 7 Applications and generalizations.- 7.1 A manifold without Kähler-Einstein metric.- 7.2 K-energy and metrics of constant scalar curvature.- 7.3 Relation to stability.
Synopsis
There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical Kähler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. This monograph gives an introduction to the theory of canonical Kähler metrics on complex manifolds. It also presents some advanced topics not easily found elsewhere., There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical K hler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. This monograph gives an introduction to the theory of canonical K hler metrics on complex manifolds. It also presents some advanced topics not easily found elsewhere., Thismonographresultsfromtheauthor'slecturesattheETHduringtheSpring Semester of 1997, when he was presenting a Nachdiplom course on Kahler Einsteinmetricsincomplexdifferentialgeometry. Therehasbeenfundamentalprogressincomplexdifferentialgeometryinthe last two decades. The uniformization theory ofcanonicalKahler metrics has beenestablishedinhigherdimensions. Manyapplicationshavebeenfound. One manifestationofthis istheuseofCalabi-Yauspacesinthesuperstringtheory. Theaimofthismonographistogiveanessentiallyself-containedintroduc tiontothetheoryofcanonicalKahlermetricsoncomplexmanifolds.Itisalso theauthor'shopetopresentthereaderswithsomeadvancedtopicsincomplex differentialgeometrywhicharehardtobefoundelsewhere. Thetopicsinclude Calabi-Futakiinvariants,ExtremalKahlermetrics,theCalabi-Yautheoremon existenceofKahler Ricci-flat metrics, and recent progresson Kahler-Einstein metricswithpositivescalarcurvature. ApplicationsofKahler-Einsteinmetrics totheuniformizationtheoryarealsodiscussed. Readers with a good general knowledge in differential geometry and par tial differential equations should be able to understand the materials in this monograph, I would like tothanktheETH for theopportunityto deliver the lectures in a very stimulating environment. In particular, I thank Meike Akveld for her patience and efficiency in taking notes ofthe lectures and producing the beautifulJb.1EXfile. Withoutherefforts,thismonographcouldneverhavebeen as it is now. I would also like to thank Ms. Nini Wong for her endless pa tienceinproof-readingandcorrectingnumeroustyposinearlierversionsofthis monograph. PartofmyworkinvolvedinthismonographwassupportedbyNationalSci enceFoundationGrantsDMS-9303999andDMS-9802479,atCourantInstitute ofMathematical Sciencesand MassachusettsInstituteofTechnology. My re searchwas alsosupportedbyaSimonsChairFundatMassachusettsInstitute ofTechnology. MIT, April 1999. GangTian Chapter1 IntroductiontoKahlermanifolds 1.1 Kahlermetrics LetM beacompact Coo manifold. ARiemannianmetricgonM isasmooth sectionofT*M @T*M definingapositivedefinitesymmetricbilinearformon TxM for each x E M. In localcoordinatesXl,...,X ,onehas anaturallocal n basis -iL,...,jL forTM, then g is represented by asmooth matrix-valued UXI UX n function {gij},where gij=g(a~i'a~j) . Notethat{gij} ispositivedefinite. Thepair(M,g) isusuallycalledaRieman nianmanifold. RecallthatanalmostcomplexstructureJ onM isabundleautomorphism ofthetangentbundleTM satisfyingj2 = - id. Definition1.1 The Nijenhuis tensorN(J) :TM xTM-+TM isgiven by N(v,w) = [v,w]+J[Jv,w]+J[v,Jw]- [Jv,Jw] forv,w vectorfields onM. Analmostcomplexstructure J on M iscalledintegrableifthere isa holo morphicstructure(thatisasetofchartswithholomorphictransitionfunctions) such that J corresponds to the induced complex multiplication in TM x C. Clearly,anycomplexstructureinducesanintegrablealmostcomplexstructure. The following theorem is due to Newlander and Nirenberg, see for example Appendix8in [14].
LC Classification Number
QA641-670
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98,7% positive Bewertungen•2,0 Mio. Artikel verkauft
Angemeldet als gewerblicher Verkäufer
Verkäuferbewertungen (523.781)
- e***n (390)- Bewertung vom Käufer.Letzter MonatBestätigter KaufGreat transaction, exactly as described, packed well, and promptly shipped on August 6th. Unfortunately the U.S. Postal Service took 23 calendar days to deliver the book. It was shipped from Pennsylvania, to Atlanta, past Alabama to Texas, enjoyed several days in Texas, then to Minneapolis, Jacksonville, Florida, back to Atlanta, finally to Birmingham, and Huntsville. The seller was very responsive and I decided it was interesting to see if/how the book would arrive. Thanks, Joe
- m***m (2338)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufI’m thrilled with my recent purchase . The website was user-friendly, and the product descriptions were accurate. Customer service was prompt and helpful, answering all my questions. My order arrived quickly, well-packaged, and the product exceeded my expectations in quality. I’m impressed with the attention to detail and the overall experience. I’ll definitely shop here again and highly recommend from this seller to others. Thank you for a fantastic experience!Tobin's Spirit Guide: Official Ghostbusters Edition by Erik Burnham: Used (Nr. 404302598631)
- _***b (57)- Bewertung vom Käufer.Letzter MonatBestätigter KaufI gave 5 stars on shipping because i sent 2 separate emails + they responded with helpful info, even though it arrived late. This was a great value with free shipping + the condition is very good, better than advertised 🙂! The overall quality and appearance is excellent! I highly recommend this seller and give them 👍👍👍👍