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Keywords:
curvature; evolutes; isoperimetric deficit; Gauss-Bonnet
curvature; evolutes; isoperimetric deficit; Gauss-Bonnet
Summary:
We relate the total curvature and the isoperimetric deficit of a curve $\gamma $ in a two-dimensional space of constant curvature with the area enclosed by the evolute of $\gamma $. We provide also a Gauss-Bonnet theorem for a special class of evolutes.
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