## Regular Patch

A regular patch is a Patch for which the Jacobian has rank 2 for all . A Patch is said to be regular at a point provided that its Jacobian has rank 2 at . For example, the points at in the standard parameterization of the Sphere are not regular.

An example of a Patch which is regular but not Injective is the Cylinder defined parametrically by with and . However, if is an injective regular patch, then x maps diffeomorphically onto .

See also Injective Patch, Patch, Regular Surface

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 187, 1993.

© 1996-9 Eric W. Weisstein
1999-05-25