Sub-Riemannian and sub-Lorentzian geometry on $\SU(1,1)$ and on its universal cover

• Main Authors: Grong, E, Vasil'ev, A
• Format: Journal Article
• Language: English
• Published: 06.10.2009
• Subjects: Mathematics - Differential Geometry; Mathematics - Optimization and Control

We study sub-Riemannian and sub-Lorentzian geometry on the Lie group $\SU(1,1)$ and on its universal cover $\CSU(1,1)$. In the sub-Riemannian case we find the distance function and completely describe sub-Riemannian geodesics on both $\SU(1,1)$ and $\CSU(1,1)$, connecting two fixed points. In partic...