Horizontal Displacement Of Curves In Bundle SO(n) -> SO_0(1,N) -> H^n

Taechang Byun

The Riemannian submersion $\pi :{\text{SO}}_0(1,n)\to {\mathbb{H}}^n$ is a principal bundle and its fiber at $\pi (e)$ is the imbedding of $\text{SO}(n)$ into ${\text{SO}}_0(1,n)$, whe…