Closed Curves in E
2 and S
2 Whose Total Squared Curvatures and Almost Minimal |
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| Authors: | Kazuyuki Enomoto |
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| Institution: | (1) Faculty of Industrial Science and Technology, Science University of Tokyo, Oshamanbe, Hokkaido, 049-35, Japan |
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| Abstract: | The total squared curvature of a closed plane curve is minimized by a covering of a circle, if the rotation number of the curve is not zero. We measure the closeness of a closed plane curve to a circle by the difference of its total squared curvature from the minimum. A similar result is obtained for a simple closed curve in the 2-sphere. |
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| Keywords: | closed curve total curvature |
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