Differential Geometry I: Worksheet 1 - Freie Universität Berlin
Differential Geometry I: Worksheet 1 - Freie Universität Berlin
Differential Geometry I: Worksheet 1 - Freie Universität Berlin
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1. Show that for the curvature the following formula holds<br />
(t) =<br />
_x(t)y(t) x(t) _y(t)<br />
:<br />
( _x(t) 2 + _y(t) 2 ) 3<br />
2<br />
2. Let R be an orientation preserving rigid motion of R 2 ; i.e.<br />
R(x; y) = M x<br />
y<br />
+ a<br />
b<br />
where M 2 SO(2) and a; b 2 R. Show that R c has the same curvature<br />
as c.<br />
;
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