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020			_a9780821891148 _q(electronic bk.)
020			_z9780821869253
035			_a(MiAaPQ)EBC3114582
035			_a(Au-PeEL)EBL3114582
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040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA649 -- .K446 2012eb
082	0		_a516.3/73
100	1		_aKhemar, Idrisse.
245	1	0	_aElliptic Integrable Systems : _bA Comprehensive Geometric Interpretation.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2012.
264		4	_c©2012.
300			_a1 online resource (234 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.219
505	0		_aIntro -- 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		_a2.3.1. 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		_a4.3.3. 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		_a6.2.5. 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		_a7.7.3. 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			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic 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	_aGeometry, Riemannian.
650		0	_aHermitian structures.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aKhemar, Idrisse _tElliptic Integrable Systems _dProvidence : American Mathematical Society,c2012 _z9780821869253
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114582 _zClick to View
999			_c70077 _d70077