HYPERKAEHLER MANIFOLD WITH LARGE SYMMETRY AND INSTANTON MODULI

具有大对称性和瞬时模量的 HYPERKAEHLER 流形

• 批准号: 10640203
• 负责人: NITTA Takashi
• 金额: $ 1.41万
• 依托单位: MIE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640203/
• 关键词: hyperkaehler; principal bundle; quaternionic structure; connection; quaternionic Kaehler; regularity; set theory; non-well-founded; hyper kahler; quater nion; Sp(1)^n-対称性; 計量; Hamilton; 四元数; ハイパーケラー; 行列値微分方程式; null correlation; ケーラー計量; L

(i) Let N be an n-dimensional Riemannin manifold and let M be an Sp(1)*n-principal bundle on N. Then an Sp(1)*n connection on M is written asTM=H+V (H=TN, V=sp(1)*n).We put a quaternionic structure I,J,K on M satisfying the condition : IH+JH+KH=V. We obtain conditions such that the quaternionic structure is hyperkaehlerian. Especially if N is R*n, we obtain equations associated with the conditions.(ii) Axiom of regularity is in Zermelo-Fraenkel set theory. Non-well-founded set theory is a set theory in which the axiom of regularity is not. Aczel, Scott, Finster, Boffa set theories are examples of non-well-founded set theories. When we let sets and ∈ corresponded to nodes and ←, each set is associated with a graph. We calculae the number of sets of Scott and Boffa set theories for node number 1,2,3.

（i）让n为n维riemannin歧管，让m成为n的sp（1）*n-主要捆绑包。我们获得的条件使Quaternionic结构是Hyperkaehlerian。特别是如果n为r*n，我们获得与条件相关的方程式。（ii）规律性的公理在zermelo-fraenkel集理论中。非孔基于的集合理论是一种集合理论，其中规律性的公理不是。 Aczel，Scott，Finster，Boffa设定理论是非井井有其的套装理论的示例。当我们让集合和∈对应于节点和←←时，每个集合都与图相关联。我们计算了Scott和Boffa的集合设定节点编号1,2,3的理论的数量。

项目成果

新田貴士、谷口正: "インスタントンモジュライ空間のL_2計量"第45回幾何学シンポジウム報告集. 295-300 (1998)

Takashi Nitta、Tadashi Taniguchi：“瞬时模空间的 L_2 度量”第 45 届几何研讨会论文集 295-300（1998）。

Nitta, T. Taniguchi, T.: "Sp(1)^n-invariant hyperkahler, quaternionic Kahler manifold"Proceeding of the second Meeting on Quaternionic Structures in Math. and Phys., Roma 6-10 Sep. 1999. (2000)

Nitta, T. Taniguchi, T.：“Sp(1)^n-不变超卡勒，四元卡勒流形”数学四元结构第二次会议论文集。

Nitta, T., Taniguchi, T.: "Kahler metric for moduli spaces of null correlation bundles"J. Math. Physis.. (2000)

Nitta, T.，Taniguchi, T.：“零相关束模空间的卡勒度量”J。

NITTA,Takashi and TANIGUCHI Tadashi: "kaehler metric for moduli spaces of null correlation bundles"J. Math. Physics. (printing now). (2000)

NITTA，Takashi 和 TANIGUCHI Tadashi：“零相关束模空间的凯勒度量”J.

NITTA,Takashi and TANIGUCHI Tadashi: "L2 metric on Instanton moduli spaces"Proceedings of the 45th geometric symposium 1998. (1998)

NITTA、Takashi 和 TANIGUCHI Tadashi：“Instanton 模空间上的 L2 度量”1998 年第 45 届几何研讨会论文集。（1998）