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Complex sprays and complex curves.

Colum Watt (2001)

Revista Matemática Complutense

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.

Compositions, Generated by Special Nets in Affinely Connected Spaces

Zlatanov, Georgi (2002)

Serdica Mathematical Journal

Special nets which characterize Cartesian, geodesic, Chebyshevian, geodesic- Chebyshevian and Chebyshevian-geodesic compositions are introduced. Con- ditions for the coefficients of the connectedness in the parameters of these special nets are found.

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