| Co-Investigator(Kenkyū-buntansha) |
SAWADA Hideki Yamagata Univ. Faculty of Science Associate Professor, 理学部, 助教授 (30095856)
II Kiyotaka Yamagata Univ. Faculty of Science Associate Professor, 理学部, 助教授 (10007180)
KAWAMURA Shinzo Yamagata Univ. Faculty of Science Professor, 理学部, 教授 (50007176)
UENO Keisuke Yamagata Univ. Faculty of Science Research Associate, 理学部, 助手 (10250911)
UCHIDA Yoshiaki Yamagata Univ. Faculty of Science Associate Professor, 理学部, 助教授 (80280890)
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| Research Abstract |
In a previous project, F.Uchida have studied smooth Sp(p, q)-actions on S^<4p+4q-1>, each of which is an extension of the standard Sp(p) × Sp(q) action on S^<4p+4q-1>. This standard action has codimension-one principal orbits with Sp(p - 1) × Sp(q - 1) as the principal isotropy subgroup. Furthermore, the fixed point set of the restricted Sp(p - 1) × Sp(q -1) action is diffeomorphic to the seven-sphere S^7.
In this project, as a main theme, we finished the study on smooth Sp(p, q) -actions on S^<4p+4q-1>. We can show such Sp(p, q)-action on S^<4p+4q-1> is characterized by a pair (φ, f) satisfying certain conditions, where φis a smooth Sp(1, 1)-action on S^7, and f : S^7 →P_1(H) is a smooth function.
The pair (φ, f) was introduced by T.Asoh to consider smooth SL(2, C) -actions on the 3-sphere, and was improved by F.Uchida.
Moreover, we obtain certain results on smooth SL(m, R) × SL(n, R) -actions on the m + n - 1-sphere and on smooth C^* × SO(n, C) -actions on the 2n - 1-sphere.
As related topics, S.Kawamura has obtained a result on chaotic maps on a measure space and behavior of the orbit of a state, K.Ii has obtained a result on the equivalence of two complex structures on the punctured tangent bundle of comlex projective space, H.Sawada has obtained a result on RSA cryptosystems, Y.Uchida has obtained a result on periodic knots with unknotting number one and K.Uene has obtained a result on proper harmonic maps from complex hyperbolic spaces into real hyperbolic spaces.
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