Elliptic integrable systems : a comprehensive geometric interpretation / / Idrisse Khemar

• Autore: Khemar Idrisse <1979->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2012; ©2012
• Descrizione fisica: 1 online resource (215 p.)
• Disciplina: 516.3/73
• Soggetto topico: Geometry, Riemannian; Hermitian structures
• Note generali: "September 2012, Volume 219, Number 1031 (fourth of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""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""; ""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""
• Titolo autorizzato: Elliptic integrable systems
• ISBN: 0-8218-9114-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910788606603321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Volume 219, Number 1031.