Show that the cylinder {$\displaystyle (x,y,z)$ in $\displaystyle R^3; x^2+y^2=1$} is a regular surface, and find parametrizations whose coordinate neighborhoods cover it.

Please help.

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- Oct 4th 2008, 02:56 PMdori1123regular surface
Show that the cylinder {$\displaystyle (x,y,z)$ in $\displaystyle R^3; x^2+y^2=1$} is a regular surface, and find parametrizations whose coordinate neighborhoods cover it.

Please help. - Oct 16th 2008, 05:05 PMwhipflip15
I won't do it for you but..

Parameterize it using cylindrical coordinates into some parameterization S.

To show it is regular you can

-Show the first partial derivative of S are independant.

or

-Show that the cross product of the first partial derivatives of S is non zero

there are many other ways to show it is regular.