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.
