After defining what is meant by a complex spray X on a complex manifold M, we introduce the notion of a spray complex curve associated to X. Several equivalent formulations are derived and we give necessary and sufficient conditions for M to admit spray complex curves for X through each point and in each direction. Refinements of this result are then derived for some special cases, for example when X is the horizontal radial vector field associated to a complex Finsler metric.
@article{urn:eudml:doc:44465,
title = {Complex sprays and complex curves.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {14},
year = {2001},
pages = {147-173},
zbl = {1024.53015},
mrnumber = {MR1851727},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44465}
}
Watt, Colum. Complex sprays and complex curves.. Revista Matemática de la Universidad Complutense de Madrid, Tome 14 (2001) pp. 147-173. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44465/