Generalized planar curves and quaternionic geometry
| Authors | |
|---|---|
| Year of publication | 2006 |
| Type | Article in Periodical |
| Magazine / Source | Annals of Global Analysis and Geometry |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007/s10455-006-9023-y |
| Field | General mathematics |
| Keywords | planar curves; quaternionic geometry; generalized geodetics |
| Attached files | |
| Description | Motivated by the analogies between the projective and the almost quaternionic geometries, we first study the generalizd planar curves and mappings. We follow, recover, and extend the classical approach. Then we exploit the impact of the general results in the almost quaternionic geometry. In particular, we show, that the natural class of H-planar curves coincides with the class of all geodesics of the so called Weyl connections and preserving this class turns out to be the necessary and sufficient condition on diffeomorphisms to become morphisms of almost quaternionic geometries. |
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