An injective patch is a patch such that implies that and . An example of a patch which is injective but not regular is the function defined by for . However, if is an injective regular patch, then maps diffeomorphically onto .
Injective Patch
See also
Patch, Regular PatchExplore with Wolfram|Alpha
References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, p. 273, 1997.Referenced on Wolfram|Alpha
Injective PatchCite this as:
Weisstein, Eric W. "Injective Patch." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InjectivePatch.html