Quaternion-based generalization of conformal maps
Abstract
For the conformal map in two dimensions, the local rescaling factor of metric amounts to that of surface element. To avoid the restriction on the functional form of the metric in d dimensions (d > 2), we generalize the conformal map in such a way that the volume element (d form), not the metric (quadratic form), is invariant up to local rescaling. For d = 4, quaternions are available to formulate such a generalized conformal map, as complex analysis is useful for the conventional conformal map.
- Publication:
-
Journal of Physics Conference Series
- Pub Date:
- April 2019
- DOI:
- 10.1088/1742-6596/1194/1/012064
- Bibcode:
- 2019JPhCS1194a2064K