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@article{699297, author = {Slovák, Jan and Hrdina, Jaroslav}, article_number = {29}, keywords = {planar curves; quaternionic geometry; generalized geodetics}, language = {eng}, issn = {0232-704X}, journal = {Annals of Global Analysis and Geometry}, title = {Generalized planar curves and quaternionic geometry}, url = {https://link.springer.com/article/10.1007/s10455-006-9023-y}, volume = {2006}, year = {2006} }
TY - JOUR ID - 699297 AU - Slovák, Jan - Hrdina, Jaroslav PY - 2006 TI - Generalized planar curves and quaternionic geometry JF - Annals of Global Analysis and Geometry VL - 2006 IS - 29 SP - 349-360 EP - 349-360 PB - Springer SN - 0232704X KW - planar curves KW - quaternionic geometry KW - generalized geodetics UR - https://link.springer.com/article/10.1007/s10455-006-9023-y L2 - https://link.springer.com/article/10.1007/s10455-006-9023-y N2 - 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. ER -
SLOVÁK, Jan and Jaroslav HRDINA. Generalized planar curves and quaternionic geometry. \textit{Annals of Global Analysis and Geometry}. Springer, 2006, vol.~2006, No~29, p.~349-360. ISSN~0232-704X.
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