An entire curve in a complex manifold 
is a holomorphic map 
. It may be constant, and need not be an embedding.
In discussions of hyperbolicity, the term is often reserved for nonconstant maps
(Diverio 2021). It is an immersion when its derivative never vanishes. For example,
defines an
entire curve in 
. Prescribing its value
and derivative at a point is a first-jet interpolation condition.
Density in the ordinary complex topology is stronger than Zariski density in a projective target.
