Geodesic
Almost complex projective structures and their morphisms
Archivum mathematicum, Tome 45 (2009) no. 4, pp. 255-264 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 53B10, 53C15
Keywords: linear connection; geodetics; $F$-planar; $A$-planar; parabolic geometry; Cartan geometry; almost complex structure; projective structure 
@article{ARM_2009_45_4_a2,
     author = {Hrdina, Jaroslav},
     title = {Almost complex projective structures and their morphisms},
     journal = {Archivum mathematicum},
     pages = {255--264},
     year = {2009},
     volume = {45},
     number = {4},
     mrnumber = {2591680},
     zbl = {1212.53022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2009_45_4_a2/}
}
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Hrdina, Jaroslav. Almost complex projective structures and their morphisms. Archivum mathematicum, Tome 45 (2009) no. 4, pp. 255-264. http://geodesic.mathdoc.fr/item/ARM_2009_45_4_a2/