11. The result is known as a homogeneous space . 12. There are many further homogeneous spaces of the classical linear groups in common use in mathematics. 13. This quotient formulation gives \ mathrm { AdS } _ n the structure of a homogeneous space . 14. Similarly, the matrices could be taken as automorphisms of a homogeneous space ; this defines a geometric finite automaton. 15. In other words, the " traditional spaces " are homogeneous spaces ; but not for a uniquely determined group. 16. The extra differential structure that these homogeneous spaces possess allows one to study and generalize their geometry using calculus. 17. In this case the non-compact space is the unit disk, a homogeneous space for SU ( 1, 1 ). 18. These equations contain only functions of time; this is a condition that has to be fulfilled in all homogeneous spaces . 19. It may be identified with the homogeneous space of complex dimension " n ( n + 1 ) / 2" 20. Using the identification of with the homogeneous space , the connection 1-form is just a component of the Maurer Cartan 1-form on.
