Information om | Engelska ordet HYPERKÄHLER

Exempel på hur man kan använda HYPERKÄHLER i en mening

• A hyperkähler manifold is a Riemannian manifold whose holonomy group is contained in the symplectic group.
• In differential geometry, self-dual Einstein 4-manifolds are also known as (4-dimensional) hyperkähler manifolds in the Ricci-flat case, and quaternion Kähler manifolds otherwise.
• Compact hyperkähler manifolds have been extensively studied using techniques from algebraic geometry, sometimes under the name holomorphically symplectic manifolds.
• Amongst his notable discoveries are the Hitchin–Thorpe inequality; Hitchin's projectively flat connection over Teichmüller space; the Atiyah–Hitchin monopole metric; the Atiyah–Hitchin–Singer theorem; the ADHM construction of instantons (of Michael Atiyah, Vladimir Drinfeld, Hitchin, and Yuri Manin); the hyperkähler quotient (of Hitchin, Anders Karlhede, Ulf Lindström and Martin Roček); Higgs bundles, which arise as solutions to the Hitchin equations, a 2-dimensional reduction of the self-dual Yang–Mills equations; and the Hitchin system, an algebraically completely integrable Hamiltonian system associated to the data of an algebraic curve and a complex reductive group.
• Ben-Zvi, Heluani, and Szczesny showed that a Riemannian metric on the manifold induces an N=1 superconformal structure, which is promoted to an N=2 structure if the metric is Kähler and Ricci-flat, and a hyperkähler structure induces an N=4 structure.
• He was one of the co-inventors of hyperkähler quotients, a hyperkahler analogue of Marsden–Weinstein reduction and the structure of Bihermitian manifolds.
• He was one of the co-inventors of hyperkähler quotients, a hyperkahler analogue of Marsden–Weinstein reduction and the structure of Bihermitian manifolds.
• The Hopf surface is the only compact hypercomplex manifold of quaternionic dimension 1 which is not hyperkähler.
• More specifically the global analysis, geometry, topology and arithmetic of hyperkähler manifolds, Yang–Mills instantons, non-Abelian Hodge theory, Geometric Langlands program, and representation theory of quivers and Kac–Moody algebras.
• A hyperkähler manifold is simultaneously a hypercomplex manifold and a quaternionic Kähler manifold.
• Isabel Graciela Dotti de Miatello (born 1947) is an Argentine mathematician specializing in the connections between group theory and differential topology, including the theory of complex nilmanifolds, nilpotent Lie groups, hypercomplex manifolds, and hyperkähler manifolds.

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