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A principal bundle with a Lie group $H$ consists of a manifold $P$ and a free proper smooth $H$-action $P\times H\to P$. There is a unique smooth manifold structure on the quotient space $M=P/H$ such that the canonical map $\pi :P\to M$ is smooth. $M$ is called a base manifold and $H\to P\to M$ stands for the bundle. The most fundamental examples of principal bundles are the homogeneous spaces $H\subset G\to G/H$, where $H$ is a closed subgroup of $G$. The pair $(𝔤,𝔥)$ is a Klein pair. A model geometry consists of a Klein pair $(𝔤,𝔥)$ and a Lie group $H$ with Lie algebra $𝔥$. In this...