parabolic element meaning in Hindi

Examples

1. This was proved by for Kleinian groups with no parabolic elements.
2. Since it is not cocompact it must then ontain parabolic elements.
3. However, if one adds the restriction that a representation must send parabolic elements in \ Gamma to parabolic elements then local rigidity holds.
4. However, if one adds the restriction that a representation must send parabolic elements in \ Gamma to parabolic elements then local rigidity holds.
5. This is a classification into " subsets, " not " subgroups : " these sets are not closed under multiplication ( the product of two parabolic elements need not be parabolic, and so forth ).
6. A more general version of Bers's conjecture due to Sullivan and Thurston states that every finitely generated Kleinian group is an algebraic limit of geometrically finite Kleinian groups . proved this for freely indecomposable Kleinian groups without parabolic elements.
7. Devices to which Winston's name has become attached include the CPC itself, which is sometimes known as a " Winston solar collector ", and " Winston cones ", the individual parabolic elements that make up a CPC.
8. Topologically, as trace is a continuous map, the elliptic elements ( excluding ? ) are an open set, as are the hyperbolic elements ( excluding ? ), while the parabolic elements ( including ? ) are a closed set.
9. The identity element 1 and negative identity element-1 ( in PSL ( 2, "'R "') they are the same ), have trace ?, and hence by this classification are parabolic elements, though they are often considered separately.
10. The simplest case is when the manifold does not have " cusps " ( i . e . the fundamental group does not contain parabolic elements ), in which a manifold is geometrically finite of and only if it is the quotient of a closed, convex subset of hyperbolic space by a group acting cocompactly on this subset.