Abstract
In this paper, we construct two-step nilpotent Lie groups from homogeneous fiber bundles over compact symmetric spaces. The structure of the constructed nilpotent groups is expressed in terms of the compact Lie groups involved in the fiber bundles. There are close relations between the geometric properties of the nilpotent groups and the total spaces of the fiber bundles. We will find new examples of nilpotent groups which are weakly symmetric and Riemannian geodesic orbit spaces.
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Tamaru, H. Two-Step Nilpotent Lie Groups and Homogeneous Fiber Bundles. Annals of Global Analysis and Geometry 24, 53–66 (2003). https://doi.org/10.1023/A:1024241806100
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DOI: https://doi.org/10.1023/A:1024241806100