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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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