Elliptic Integrable Systems : (Record no. 70077)
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| fixed length control field | 09960nam a22005053i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC3114582 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729124612.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2012 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780821891148 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780821869253 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC3114582 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL3114582 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11041360 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)922964993 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA649 -- .K446 2012eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.3/73 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Khemar, Idrisse. |
| 245 10 - TITLE STATEMENT | |
| Title | Elliptic Integrable Systems : |
| Remainder of title | A Comprehensive Geometric Interpretation. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2012. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2012. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (234 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society ; |
| Volume/sequential designation | v.219 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Intro -- Contents -- Abstract -- Introduction -- 0.1. The primitive systems -- 0.2. The determined case -- 0.2.1. The minimal determined system -- 0.2.2. The general structure of the maximal determined case -- 0.2.3. The model system in the even case -- 0.2.4. The model system in the odd case -- 0.2.5. The coupled model system -- 0.2.6. The general maximal determined odd system (k'=2k+1,m=2k) -- 0.2.7. The general maximal determined even system (k'=2k,m=2k-1) -- 0.2.8. The intermediate determined systems -- 0.3. The underdetermined case -- 0.4. In the twistor space -- 0.5. Related subjects and works, and motivations -- 0.5.1. Relations with surface theory -- 0.5.2. Relations with mathematical physics -- 0.5.3. Relations of F-stringy harmonicity and supersymmetry -- Notation, conventions and general definitions -- 0.6. List of notational conventions and organisation of the paper -- 0.7. Almost complex geometry -- Chapter 1. Invariant connections on reductive homogeneous spaces -- 1.1. Linear isotropy representation -- 1.2. Reductive homogeneous space -- 1.3. The (canonical) invariant connection -- 1.4. Associated covariant derivative -- 1.5. G-invariant linear connections in terms of equivariant bilinear maps -- 1.6. A family of connections on the reductive space M -- 1.7. Differentiation in End(T(G/H)) -- Chapter 2. m-th elliptic integrable system associated to a k'-symmetric space -- 2.0.1. Definition of G (even when does not integrate in G) -- 2.1. Finite order Lie algebra automorphisms -- 2.1.1. The even case: k'=2k -- 2.1.2. The odd case: k'=2k+1 -- 2.2. Definitions and general properties of the m-th elliptic system -- 2.2.1. Definitions -- 2.2.2. The geometric solution -- 2.2.3. The increasing sequence of spaces of solutions: (S(m))mN -- 2.2.4. The decreasing sequence (Syst(m,p))p/k' -- 2.3. The minimal determined case. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 2.3.1. The even minimal determined case: k'=2k and m=k -- 2.3.2. The minimal determined odd case -- 2.4. The maximal determined case -- Adding holomorphicity conditions -- the intermediate determined systems -- 2.5. The underdetermined case -- 2.6. Examples -- 2.6.1. The trivial case: the 0-th elliptic system associated to a Lie group -- 2.6.2. Even determined case -- 2.6.3. Primitive case -- 2.6.4. Underdetermined case -- 2.7. Bibliographical remarks and summary of the results -- Chapter 3. Finite order isometries and twistor spaces -- 3.1. Isometries of order 2k with no eigenvalues =1 -- 3.1.1. The set of connected components in the general case -- 3.1.2. Study of Ad J, for JZ2ka(R2n) -- 3.1.3. Study of Ad Jj -- 3.2. Isometries of order 2k+1 with no eigenvalue =1 -- 3.3. The effect of the power maps on the finite order isometries -- 3.4. The twistor spaces of a Riemannian manifolds and its reductions -- 3.5. Return to an order 2k automorphism 2mu-:6muplus1mugg -- 3.5.1. Case r=k -- 3.5.2. Action of Ad|m on adgjC -- 3.6. The canonical section in (Z2k(G/H))2, the canonical embedding, and the twistor lifts -- 3.6.1. The canonical embedding -- 3.6.2. The twistor lifts -- 3.7. Bibliographical remarks and summary of the results -- Chapter 4. Vertically harmonic maps and harmonic sections of submersions -- 4.1. Definitions, general properties and examples -- 4.1.1. The vertical energy functional -- 4.1.2. Examples -- 4.1.3. -torsion, -difference tensor, and curvature of a Pfaffian system -- 4.2. Harmonic sections of homogeneous fibre bundles -- 4.2.1. Definitions and geometric properties -- 4.2.2. Vertical harmonicity equation -- 4.2.3. Reductions of homogeneous fibre bundles -- 4.3. Examples of homogeneous fibre bundles -- 4.3.1. Homogeneous spaces fibration -- 4.3.2. The twistor bundle of almost complex structures (E). |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4.3.3. The twistor bundle Z2k(E) of a Riemannian vector bundle -- 4.3.4. The twistor subbundle Z2k,j(E) -- 4.4. Geometric interpretation of the even minimal determined system -- 4.4.1. The injective morphism of homogeneous fibre bundle -- 4.4.2. Conclusion -- 4.5. Bibliographical remarks and summary of the results -- Chapter 5. Generalized harmonic maps -- 5.1. Affine harmonic maps and holomorphically harmonic maps -- 5.1.1. Affine harmonic maps: general properties -- 5.1.2. Holomorphically harmonic maps -- 5.2. The sigma model with a Wess-Zumino term in nearly Kähler manifolds -- 5.2.1. Totally skew-symmetric torsion -- 5.2.2. The general case of an almost Hermitian manifold -- 5.2.3. The example of a 3-symmetric space -- 5.2.4. The good geometric context/setting -- 5.2.5. J-twisted harmonic maps -- 5.3. The sigma model with a Wess-Zumino term in G1-manifolds -- 5.3.1. TN-valued 2-forms -- 5.3.2. Stringy harmonic maps -- 5.3.3. Almost Hermitian G1-manifolds -- 5.3.4. Characterization of Hermitian connections in terms of their torsion -- 5.3.5. The example of a naturally reductive homogeneous space -- 5.3.6. Geometric interpretation of the maximal determined odd case -- 5.4. Stringy harmonicity versus holomorphic harmonicity -- 5.5. Bibliographical remarks and summary of the results -- Chapter 6. Generalized harmonic maps into f-manifolds -- 6.1. f-structures: General definitions and properties -- 6.1.1. f-structures, Nijenhuis tensor and natural action on the space of torsions T -- 6.1.2. Introducing a linear connection -- 6.2. The f-connections and their torsion -- 6.2.1. Definition, notation and first properties -- 6.2.2. Characterization of metric connections preserving the splitting -- 6.2.3. Characterization of metric f-connections. Existence of a characteristic connection -- 6.2.4. Precharacteristic and paracharacteristic connections. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.2.5. Reductions of f-manifolds -- 6.3. f-connections on fibre bundles -- 6.3.1. Riemannian submersion and metric f-manifolds of global type G1 -- 6.3.2. Reductions of f-submersions -- 6.3.3. Horizontally Kähler f-manifolds and horizontally projectible f-submer-sions -- 6.3.4. The example of a naturally reductive homogeneous space -- 6.3.5. The example of the twistor space Z2k(M) -- 6.3.6. The example of the twistor space Z2k,j(M,Jj) -- 6.3.7. The reduction of homogeneous fibre bundle IJ0: G/G0-3muZ2k,20(G/H,J2) -- 6.4. Stringy harmonic maps in f-manifolds -- 6.4.1. Definitions -- 6.4.2. The closeness of the 3-forms FT and FT -- 6.4.3. The sigma model with a Wess-Zumino term in reductive metric f-manifold of global type G1 -- 6.4.4. The example of a naturally reductive homogeneous space -- 6.4.5. Geometric interpretation of the maximal determined even case -- 6.4.6. Twistorial geometric interpretation of the maximal determined even case -- 6.4.7. About the variational interpretation in the twistor spaces -- 6.5. Bibliographical remarks and summary of the results -- Chapter 7. Generalized harmonic maps into reductive homogeneous spaces -- 7.1. Affine harmonic maps into reductive homogeneous spaces -- Affine harmonic maps into symmetric spaces -- 7.2. Affine/holomorphically harmonic maps into 3-symmetric spaces -- 7.3. (Affine) vertically (holomorphically) harmonic maps -- 7.3.1. Affine vertically harmonic maps: general properties -- 7.3.2. Affine vertically holomorphically harmonic maps -- 7.4. Affine vertically harmonic maps into reductive homogeneous space -- The Riemannian case -- 7.5. Harmonicity vs. vertical harmonicity -- 7.6. (Affine) vertically (holomorphically) harmonic maps into reductive homogeneous space with an invariant Pfaffian structure -- 7.7. The intermediate determined systems -- 7.7.1. The odd case -- 7.7.2. The even case. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 7.7.3. Sigma model with a Wess-Zumino term -- 7.8. Some remarks about the twistorial interpretation -- 7.8.1. The even case -- 7.8.2. The odd case -- 7.9. Bibliographical remarks and summary of the results -- Chapter 8. Appendix -- 8.1. Vertical harmonicity -- 8.2. G-invariant metrics -- 8.2.1. About the natural reductivity -- 8.2.2. Existence of an Ad H-invariant inner product on k for which |m is an isometry -- 8.2.3. Existence of a naturally reductive metric for which J is an isometry, resp. F is metric -- Bibliography -- Index -- List of symbols -- Section 1 -- Section 2 -- Section 3 -- Section 4 -- Section 5 -- Section 6 -- Section 7. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Geometry, Riemannian. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Hermitian structures. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Khemar, Idrisse |
| Title | Elliptic Integrable Systems |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2012 |
| International Standard Book Number | 9780821869253 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114582">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114582</a> |
| Public note | Click to View |
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