| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
In this research, we have studied proper actions and discontinuous groups for symmetric spaces. The most valuable result in this research is the following: we found deep relationships between the study of proper actions on pseudo-Riemannian symmetric spaces and that of conjugacy classes of totally geodesic submanifolds in non-compact Riemannian symmetric spaces. Totally submanifolds in symmetric spaces can be understood by Lie algebras and root systems (a kind of combinatorics objects) in some sense. In particular, we give a definition of ``Dynkin indices'' of totally geodesic submanifolds in symmetric spaces in terms of sectional curvatures and applied it to the study of proper actions on pseudo-Riemannian symmetric spaces.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究のテーマである対称空間上の固有な群作用, 不連続群は, 微分幾何学における主要な研究分野の一つである. 本研究の成果により, 特に擬リーマン対称空間上の不連続群という取扱いの難しい現象が, リーマン対称空間の全測地的部分多様体(``平面内の直線''や``空間内の平面''などの一般化)と呼ばれる基本的な対象の研究と深く関連することが分かった. これはこの研究分野における重要な知見であると思われる.
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