Super Kohler manifold

As a result of having compared it with the original, it becomes clear for this article that there is mistranslation a lot (more than at least five). Please be careful about the use of the information. I find the one that can change translation in a correct phrase.

References and the source which I can inspect are not shown at all, or this article is insufficient. You add the source, and please cooperate with the reliability improvement of the article. (September, 2015)

Super Kohler manifold (hyperkähler manifold) is Lehman manifold of the dimension 4k dimension and, in differential geometry, says the case that ホロノミー group (English version) (holonomy group) includes Sp(k) in (and Sp(k) expresses compact form of the シンプレクティック group here${\displaystyle k}$-) which is identified with a group of the 4 yuan number line model ユニタリ self associate same model of the number of dimensional 4 yuan L meat space. I can regard the super Kohler manifold as the number of 4 yuan of the Kohler manifold in the special class of the Kohler manifold. It is Kalla biヤウ manifold that all super Kohler manifolds are rich flatness and therefore understand it easily because Sp(k) is subgroup of SU(2k).

The super Kohler manifold was defined in エウジェニオ Kalla biにより 1978.

Table of contents

Number of 4 yuan structure

Super Kohler manifold M is a two-dimensional spherical surface with double bare structure than a measurement being Kohler (having 概複素構造 which, in other words, is integrability).

Particularly, such a manifold is 概四元数多様体, and three different double bare structure I, J, K exists; a 4 yuan numerical expression of relations

${\displaystyle I^{2}=J^{2}=K^{2}=IJK=-1\,}$ 

I satisfy を. Real number ${\displaystyle a,b,c}$  But

${\displaystyle a^{2}+b^{2}+c^{2}=1\,}$ 

Any linear combination when it was said that I satisfied を

${\displaystyle aI+bJ+cK\,}$ 

It is もまた, double bare structure on M. Particularly, 接空間 T_xM is a number of 4 yuan vector space in each point x. Sp(k) is linear about I, J, K ${\displaystyle \mathbb {R} ^{4k}=\mathbb {H} ^{k}}$  I can think with の orthogonality conversion group. From this, I understand that ホロノミー of the manifold is included in Sp(k). On the contrary, if ホロノミー group of Lehman manifold M is included in Sp(k), I choose double bare structure I_x, J_x, K_x in T_xM and can represent T_xM in a number of 4 yuan vector space. The translation of these double bare structure brings number of 4 yuan manifold structure on M finding.

The シンプレクティック form that is ホロノミック

Super Kohler manifold (M,I,J,K) is the シンプレクティック manifold which is Masanori when I think with double bare manifolds (M,I) (with non-degeneration 2 - form that is Masanori). In the case of a compact manifold, it was shown in proof of the Kalla biexpectation of ヤウ that the reverse was also right. When シンプレクティック manifold (M,I) which is Kohler is given with a compact, I always have super Kohler measurements with consistency. Such a measurement is one idea for given Kohler class. The compact Kohler manifold is expanded using technique from algebra geometry and is studied and may be called Masanori シンプレクティック geometry. In the ホロノミー group of Masanori シンプレクティック manifold M which is compact by ボゴモロフ (English version) (Bogomolov) resolution theorem (1974), it is the equivalent that a scalar increases twice as much the pair of the arbitrary Masanori シンプレクティック form on M by a single connection each other thing and M which just become Sp(k).

Example

By the resolution of Kodaira of double bare curved surfaces, any compact four-dimensional super Kohler manifold is K3 curved surface or a compact torus ${\displaystyle T^{4}}$  である. (because SU(2) is Sp(1) and the same model, all four-dimensional Kalla biヤウ manifolds are super Kohler manifolds.)

The Hilbert scheme of the point in the four-dimensional compact super Kohler manifold is super Kohler manifold. This brings two serieses for a compact example. With the Hilbert scheme of the point on the K3 curved surface [Hilbert scheme | generalization クンマー manifold]] である.

I express the number of 4 yuan in H, and G is known to four dimensions of super Kohler manifolds which is perfection for an asymptotic non-compact to H/G as asymptotic local site Euclidean space (English version) (asymptotically locally Euclidean) or ALE space as limited subgroup of Sp(1). Various generalization by the asymptotic behavior unlike these space is studied by a name of the gravity instanton in physics. Gibbons Hawking temporary construction (English version) (Gibbons–Hawking ansatz) brings the example unchangeable below for the sheathed rounded sword.

As for the example of many non-compact super Kohler manifolds, one of a solution of the gauge theory that there is to be provided from the dimension conciseness of the 自己双対 Jan Milnes equation occurs from the space in July. I include インスタントンモジュライ space, モノポールモジュライ space, the space of the solution of 自己双対方程式 in the Riemannian surface of ヒッチン, the space of the solution of the ナーム equation. As another example, there is very important 中島箙多様体 (English version) (Nakajima quiver varieties) for an expression theory.

Allied item

• Number of 4 yuan Kohler manifold (English version) (Quaternionic-Kähler manifold)
• Super double bare manifolds (English version) (Hypercomplex manifold)
• Kalla biヤウ manifold

Outside link

• Maciej Dunajski and Lionel J. Mason, (2000), "Hyper Kahler Hierarchies and their Twistor Theory"

It is acquired by "https://ja.wikipedia.org/w/index.php?title= super Kohler manifold &oldid=56986867"

This article is taken from the Japanese Wikipedia Super Kohler manifold

This article is distributed by cc-by-sa or GFDL license in accordance with the provisions of Wikipedia.

Wikipedia and Tranpedia does not guarantee the accuracy of this document. See our disclaimer for more information.

In addition, Tranpedia is simply not responsible for any show is only by translating the writings of foreign licenses that are compatible with CC-BY-SA license information.