A patch (also called a Local Surface) is a differentiable mapping
, where is an
open subset of . More generally, if is any Subset of , then a map
is a patch provided that can be extended to a differentiable map from into ,
where is an open set containing . Here, (or more generally, ) is called the
Trace of **x**.

**References**

Gray, A. ``Patches in .'' §10.2 in *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 183-184 and 192-193, 1993.

© 1996-9

1999-05-26