Publication detail

Generalized planar curves and quaternionic geometry.

HRDINA, J. SLOVÁK, J.

English title

Generalized planar curves and quaternionic geometry.

Type

journal article in Web of Science

Language

en

Original abstract

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. Anotace anglicky: 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.

English abstract

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. Anotace anglicky: 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.

Released

01.07.2006

Publisher

Ann. Global Anal. Geom. 29, No. 4, Springer

ISSN

0232-704X

Journal

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY

Pages from–to

349–360

Pages count

12

BIBTEX


@article{BUT49394,
  author="Jaroslav {Hrdina} and Jan {Slovák},
  title="Generalized planar curves and quaternionic geometry.",
  journal="ANNALS OF GLOBAL ANALYSIS AND GEOMETRY",
  year="2006",
  month="July",
  pages="349--360",
  publisher="Ann. Global Anal. Geom. 29, No. 4, Springer",
  issn="0232-704X"
}