HYPERKAEHLER MANIFOLD WITH LARGE SYMMETRY AND INSTANTON MODULI

(i)设N是一个n维Riemannin流形，M是N上的一个Sp（1）* n-主丛.然后将M上的一个Sp（1）n联络记为TM =H+V（H=TN，V=sp（1）n），在M上放置一个满足条件IH+JH+KH= V的四元数结构I，J，K，得到了该四元数结构是超kaehler的条件.特别是当N为R*n时，我们得到了与条件相关的方程。(ii)正则性公理是Zermelo-Fraenkel集合论中的公理。非良基集合论是一种正则性公理不成立的集合论。Aczel，Scott，Finster，博法集合论都是非良基集合论的例子。当我们让集合和∈对应于节点和←时，每个集合都与一个图相关联。计算了节点数为1，2，3时Scott和博法集合论的集合数.

(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.