hyperkähler
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Hyperkähler manifold — In differential geometry, a hyperkähler manifold is a Riemannian manifold of dimension 4 k and holonomy group contained in Sp( k ) (here Sp( k ) denotes a compact form of a symplectic group, identifiedwith the group of quaternionic linear unitary … Wikipedia
Gravitational instanton — In mathematical physics and differential geometry, a gravitational instanton is a four dimensional complete Riemannian manifold satisfying the vacuum Einstein equations. They are so named because they are analogues in quantum theories of gravity… … Wikipedia
Quaternion-Kähler manifold — In differential geometry, a quaternion Kähler manifold (or quaternionic Kähler manifold) is a Riemannian manifold whose Riemannian holonomy group is a subgroup of Sp( n )·Sp(1). Another, more explicit, definition, uses a 3 dimensional subbundle H … Wikipedia
Hilbert scheme — In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general scheme), refining the Chow variety. The Hilbert scheme is a disjoint… … Wikipedia
Hiraku Nakajima — (jap. 中島 啓, Nakajima Hiraku; * 30. November 1962 in Tokio) ist ein japanischer Mathematiker, der sich mit Darstellungstheorie, mathematischer Physik, algebraischer Geometrie und Differentialgeometrie beschäftigt. Nakjima studierte an der… … Deutsch Wikipedia
Instanton — An instanton or pseudoparticle is a notion appearing in theoretical and mathematical physics. Mathematically, a Yang Mills instanton is a self dual or anti self dual connection in a principal bundle over a four dimensional Riemannian manifold… … Wikipedia
Einstein manifold — In differential geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo Riemannian manifold whose Ricci tensor is proportional to the metric. They are named after Albert Einstein because this condition is equivalent to… … Wikipedia
Holonomy — Parallel transport on a sphere depends on the path. Transporting from A → N → B → A yields a vector different from the initial vector. This failure to return to the initial vector is measured by the holonomy of the connection. In differential… … Wikipedia
Martin Rocek — is a professor of theoretical physics at the State University of New York at Stony Brook and a member of the C. N. Yang Institute for Theoretical Physics. He received A.B. and Ph.D. degrees from Harvard University in 1975 and 1979. He did post… … Wikipedia
Hypercomplex manifold — In differential geometry, a hypercomplex manifold is a manifold with the tangent bundleequipped with an action by the algebra of quaternionsin such a way that the quaternions I, J, Kdefine integrable almost complex structures. Examples Every… … Wikipedia
