There are several somewhat different definitions of the word analytic curve depending on context. In the context of a real analytic manifold (for example ), the most generic definition is perhaps the following.
Other words for this concept are smooth analytic curve, in which case the word analytic curve would be reserved for curves with singularities. That is, for real analytic subvarieties of . Some authors will emphasize the fact that this is a real curve and say real analytic curve.
In the context of subvarieties the following definition may be used.
Note that locally all complex analytic subvarieties of dimension 1 in can be parametrized by a the Puiseux parametrization theorem. Perhaps that is why there is the confusion in using the term.
- 1 Theodore B. Gamelin. . Springer-Verlag, New York, New York, 2001.
- 2 Hassler Whitney. . Addison-Wesley, Philippines, 1972.
|Date of creation||2013-03-22 14:18:03|
|Last modified on||2013-03-22 14:18:03|
|Last modified by||jirka (4157)|
|Synonym||smooth analytic curve|
|Synonym||real analytic curve|