| 1. | The M�bius transformations are the projective transformations of the complex projective line.
|
| 2. | The cross-ratio is invariant under the projective transformations of the line.
|
| 3. | These include both affine transformations ( such as translation ) and projective transformations.
|
| 4. | The restriction of this projective transformation to the midsphere is a M�bius transformation.
|
| 5. | We see that projective transformations don't mix Gaussian curvatures of different sign.
|
| 6. | It is the study of geometric properties that are invariant with respect to projective transformations.
|
| 7. | Two matrices represent the same projective transformation if one is a constant multiple of the other.
|
| 8. | Projective transformations are represented by matrices.
|
| 9. | :Cross-ratio is a projective invariant i . e . it is unchanged by projective transformations.
|
| 10. | But I'm working with projective transformations now, and these volume elements aren't preserved.
|
मोबाइल