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$%C. Watt, Complex sprays and complex curves, Rev. Mat. Complut. 14 (2001), no. 1, 147–173.%$

Complex Sprays and Complex Curves

Colum WATT

Revised: October 2, 2000

ABSTRACT

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.

2000 Mathematics Subject Classification: 53B40, 53C56, 53C60; secondary: 30F99.