Publication detail

ALMOST COMPLEX PROJECTIVE STRUCTURES AND THEIR MORPHISMS

HRDINA, J.

Czech title

Skoro komplexní projektivní struktury a jejich morfismy.

English title

ALMOST COMPLEX PROJECTIVE STRUCTURES AND THEIR MORPHISMS

Type

journal article - other

Language

en

Original abstract

We discuss almost complex projective geometry and the relations to a distinguished class of curves. We present the geometry from the viewpoint of the theory of parabolic geometries and we shall specify the classical genera- lizations of the concept of the planarity of curves to this case. In particular, we show that the natural class of J-planar curves coincides with the class of all geodesics of the so called Weyl connections and preserving of this class turns out to be the necessary and sufficient condition on diffeomorphisms to become homomorphisms or antihomomorphisms of almost complex projective geometries.

Czech abstract

Diskutujeme skoro komlexní projektivní geometrii a její vztah k význacným trídám krivek.

English abstract

We discuss almost complex projective geometry and the relations to a distinguished class of curves. We present the geometry from the viewpoint of the theory of parabolic geometries and we shall specify the classical genera- lizations of the concept of the planarity of curves to this case. In particular, we show that the natural class of J-planar curves coincides with the class of all geodesics of the so called Weyl connections and preserving of this class turns out to be the necessary and sufficient condition on diffeomorphisms to become homomorphisms or antihomomorphisms of almost complex projective geometries.

Keywords in English

linear connection, geodetics, F -planar, A-planar, parabolic geometry, Cartan geometry, almost complex structure, projective structure.

RIV year

2009

Released

01.12.2009

ISSN

0044-8753

Journal

ARCHIVUM MATHEMATICUM

Volume

2009

Number

45

Pages from–to

325–334

Pages count

10

BIBTEX


@article{BUT46803,
  author="Jaroslav {Hrdina},
  title="ALMOST COMPLEX PROJECTIVE STRUCTURES AND THEIR MORPHISMS",
  journal="ARCHIVUM MATHEMATICUM",
  year="2009",
  volume="2009",
  number="45",
  month="December",
  pages="325--334",
  issn="0044-8753"
}