| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1999: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Research Abstract |
(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 as
TM=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.
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