About: Eguchi–Hanson space

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In mathematics and theoretical physics, the Eguchi–Hanson space is a non-compact, self-dual, asymptotically locally Euclidean (ALE) metric on the cotangent bundle of the 2-sphere T*S2. The holonomy group of this 4-real-dimensional manifold is SU(2). The metric is generally attributed to the physicists Tohru Eguchi and Andrew J. Hanson; it was discovered independently by the mathematician Eugenio Calabi around the same time in 1979. where is a scale setting constant and .

Attributes	Values
rdfs:label	Eguchi–Hanson space (en) 에구치-핸슨 공간 (ko)
rdfs:comment	이론물리학에서 에구치-핸슨 공간(Eguchi[江口]-Hanson空間, 영어: Eguchi–Hanson space)은 4차원 초켈러 다양체의 하나이며, A1 점근 국소 유클리드 공간이다. 즉, 콤팩트하지 않으며, 점근적으로 (즉, 중심에서 멀리 떨어져) 의 꼴이다. 중력적 순간자의 일종으로 해석할 수 있다. (ko) In mathematics and theoretical physics, the Eguchi–Hanson space is a non-compact, self-dual, asymptotically locally Euclidean (ALE) metric on the cotangent bundle of the 2-sphere T*S2. The holonomy group of this 4-real-dimensional manifold is SU(2). The metric is generally attributed to the physicists Tohru Eguchi and Andrew J. Hanson; it was discovered independently by the mathematician Eugenio Calabi around the same time in 1979. where is a scale setting constant and . (en)
dcterms:subject	Differential geometry String theory
Wikipage page ID	29321898 (xsd:integer)
Wikipage revision ID	1116592158 (xsd:integer)
Link from a Wikipage to another Wikipage	Holonomy group Hyperkähler manifold Resolution of singularities Differential geometry String theory Mathematics Geometry Andrew J. Hanson Calabi–Yau manifold String theory Theoretical physics Tohru Eguchi Eugenio Calabi Gravitational instanton Cotangent bundle ADE classification K3 surface Manifold Orbifold Metric signature Einstein's equations Ricci tensor Self-dual
sameAs	Eguchi–Hanson space Eguchi–Hanson space Eguchi–Hanson space Eguchi–Hanson space
dbp:wikiPageUsesTemplate	dbt:Differential-geometry-stub dbt:String-theory-stub
has abstract	In mathematics and theoretical physics, the Eguchi–Hanson space is a non-compact, self-dual, asymptotically locally Euclidean (ALE) metric on the cotangent bundle of the 2-sphere T*S2. The holonomy group of this 4-real-dimensional manifold is SU(2). The metric is generally attributed to the physicists Tohru Eguchi and Andrew J. Hanson; it was discovered independently by the mathematician Eugenio Calabi around the same time in 1979. The Eguchi-Hanson metric has Ricci tensor equal to zero, making it a solution to the vacuum Einstein equations of general relativity, albeit with Riemannian rather than Lorentzian metric signature. It may be regarded as a resolution of the A1 singularity according to the ADE classification which is the singularity at the fixed point of the C2/Z2 orbifold where the Z2 group inverts the signs of both complex coordinates in C2. The even dimensional space of dimension can be described using complex coordinates with a metric where is a scale setting constant and . Aside from its inherent importance in pure geometry, the space is important in string theory. Certain types of K3 surfaces can be approximated as a combination of several Eguchi–Hanson metrics since both have the same holonomy group. Similarly, the space can also be used to construct Calabi–Yau manifolds by replacing the orbifold singularities of with Eguchi–Hanson spaces. The Eguchi–Hanson metric is the prototypical example of a gravitational instanton; detailed expressions for the metric are given in that article. It is then an example of a hyperkähler manifold. (en) 이론물리학에서 에구치-핸슨 공간(Eguchi[江口]-Hanson空間, 영어: Eguchi–Hanson space)은 4차원 초켈러 다양체의 하나이며, A1 점근 국소 유클리드 공간이다. 즉, 콤팩트하지 않으며, 점근적으로 (즉, 중심에서 멀리 떨어져) 의 꼴이다. 중력적 순간자의 일종으로 해석할 수 있다. (ko)
prov:wasDerivedFrom	wikipedia-en:Eguchi–Hanson_space?oldid=1116592158&ns=0
page length (characters) of wiki page	3258 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Eguchi–Hanson_space
is Link from a Wikipage to another Wikipage of	Hyperkähler manifold Ricci-flat manifold Andrew J. Hanson Tohru Eguchi Eugenio Calabi Gravitational instanton Eguchi-Hanson space
is Wikipage redirect of	Eguchi-Hanson space
is foaf:primaryTopic of	wikipedia-en:Eguchi–Hanson_space

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