Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Let mathbb{B} be a Lie group admitting a left-invariant negatively curved Kählerian structure. Consider a strongly continuous action alpha of mathbb{B} on a Fréchet algebra mathcal{A}. Denote by mathcal{A}^infty the associated Fréchet algebra of smooth vectors for this action. In the Abelian case mathbb{B}=mathbb{R}^{2n} and alpha isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Fréchet algebra structures {star_{heta}^alpha}_{hetainmathbb{R}} on mathcal{A}^infty. When mathcal{A} is a C^*-algebra, every deformed Fréchet algebra (mathcal{A}^infty,star^alpha_heta) admits a compatible pre-C^*-structure, hence yielding a deformation theory at the level of C^*-algebras too. In this memoir, the authors prove both analogous statements for general negatively curved Kählerian groups. The construction relies on the one hand on combining a non-Abelian version of oscillatory integral on tempered Lie groups with geom,etrical objects coming from invariant WKB-quantization of solvable symplectic symmetric spaces, and, on the second hand, in establishing a non-Abelian version of the Calderón-Vaillancourt Theorem. In particular, the authors give an oscillating kernel formula for WKB-star products on symplectic symmetric spaces that fiber over an exponential Lie group.

Lie groups. --- Kählerian structures.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Lie groups. --- Kählerian structures. --- Groupes de Lie --- Structures kählériennes --- Lie groups --- Kählerian structures --- Kählerian structures. --- Structures kählériennes

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Kählerian manifolds. --- Manifolds (Mathematics) --- Invariants. --- Geometry, Differential. --- Differential geometry --- Geometry, Differential --- Topology --- Kählerian structures --- Kahlerian manifolds.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi-Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.

Kählerian manifolds --- Variétés kählériennes --- Kählerian manifolds. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Geometry, Differential --- Kählerian structures --- Manifolds (Mathematics) --- Kahlerian manifolds.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Relativity (Physics) --- Hermitian structures --- Kählerian structures --- Complex manifolds --- Relativité (Physique) --- Structures hermitiennes --- Structures kählériennes --- Espaces symétriques hermitiens