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 2at . 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 definedparametrically by with and . However, if isan injective regular patch, then x maps diffeomorphically onto .

References

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

• Mortal
• Mortality Problem
• Morton-Franks-Williams Inequality
• Mosaic
• Moser
• Moser's Circle Problem
• Moss's Egg
• Motzkin Number
• Moufang Plane
• Mousetrap
• Mouth
• Moving Average
• Moving Ladder Constant
• Moving Sofa Constant
• Mrs. Perkins' Quilt
• Much Greater
• Much Less
• Mu Function
• Muirhead's Theorem
• Muller's Method
• Mulliken Symbols
• Multiamicable Numbers
• Multifactorial
• Multifractal Measure
• Multigrade Equation