Generalized planar curves and quaternionic geometry

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Authors

SLOVÁK Jan HRDINA Jaroslav

Year of publication 2006
Type Article in Periodical
Magazine / Source Annals of Global Analysis and Geometry
MU Faculty or unit

Faculty of Informatics

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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