島根大学理学部紀要

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島根大学理学部紀要 18
1984-12-25 発行

等質系の包絡リー群への全測地的埋込み

Totally Geodesic Imbeddings of Homogeneous Systems into their Enveloping Lie Groups
吉川 通彦
ファイル
内容記述(抄録等)
The enveloping Lie group A = G x K_e of a connected analytic homogeneous system (G, η) contains a submanifold G x { 1 } which can be identified with G under the canonical imbedding. In this paper, we characterize the class of homogeneous systems imbedded totally geodesically into their enveloping Lie groups, carrying with their canonical connections. It is shown that the class of symmetric homogeneous systems and that of homogeneous systems of Lie groups are essentially the case, among K-semisimple homogeneous systems (Theorem 4).