# Almost complex projective structures and their morphisms

Archivum Mathematicum (2009)

- Volume: 045, Issue: 4, page 255-264
- ISSN: 0044-8753

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topHrdina, Jaroslav. "Almost complex projective structures and their morphisms." Archivum Mathematicum 045.4 (2009): 255-264. <http://eudml.org/doc/250693>.

@article{Hrdina2009,

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 generalizations 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 anti-homomorphisms of almost complex projective geometries.},

author = {Hrdina, Jaroslav},

journal = {Archivum Mathematicum},

keywords = {linear connection; geodetics; $F$-planar; $A$-planar; parabolic geometry; Cartan geometry; almost complex structure; projective structure; linear connection; geodetic; -planar; -planar; parabolic geometry; Cartan geometry; almost complex structure; projective structure},

language = {eng},

number = {4},

pages = {255-264},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Almost complex projective structures and their morphisms},

url = {http://eudml.org/doc/250693},

volume = {045},

year = {2009},

}

TY - JOUR

AU - Hrdina, Jaroslav

TI - Almost complex projective structures and their morphisms

JO - Archivum Mathematicum

PY - 2009

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 045

IS - 4

SP - 255

EP - 264

AB - 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 generalizations 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 anti-homomorphisms of almost complex projective geometries.

LA - eng

KW - linear connection; geodetics; $F$-planar; $A$-planar; parabolic geometry; Cartan geometry; almost complex structure; projective structure; linear connection; geodetic; -planar; -planar; parabolic geometry; Cartan geometry; almost complex structure; projective structure

UR - http://eudml.org/doc/250693

ER -

## References

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- Yano, K., Differential geometry on complex and almost complex spaces, The Macmillan Company NY, 1965. (1965) Zbl0127.12405MR0187181

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