arithmetic kleinian groupの例文

例文

1. As in the Fuchsian case arithmetic Kleinian groups are discrete subgroups of finite covolume.
2. The construction of arithmetic Kleinian groups from quaternion algebras gives rise to particularly interesting hyperbolic manifolds.
3. They are not cocompact, and any arithmetic Kleinian group which is not commensurable to a conjugate of a Bianchi group is cocompact.
4. Arithmetic Kleinian groups are constructed similarly except that F is required to have exactly one complex place and A to be the Hamilton quaternions at all real places.
5. The subgroups of \ mathrm { PSL } _ 2 ( \ mathbb C ) commensurable to those obtained by this construction are called " arithmetic Kleinian groups ".