The right cylinder over the circle x^2+y^2=1 has the parametrization bar x:UtoR^3, where U=(u,v)inR^2:0<u<2pi, -infty<v<infty, bar x(u,v)=(cos u,sin u,v). Then the coefficients E, F, G in the first fundamental form of the cylinder are given by:

Q58Section II (Mathematics)58 of 145

The unit cylinder is locally isometric to the plane: $E=G=1$ , $F=0$

The right cylinder over the circle $x^2+y^2=1$ has the parametrization $\bar x:U\to\mathbb{R}^3$ , where $U=\{(u,v)\in\mathbb{R}^2:0<u<2\pi, -\infty<v<\infty\}$ , $\bar x(u,v)=(\cos u,\sin u,v)$ . Then the coefficients E, F, G in the first fundamental form of the cylinder are given by:

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