论文信息 - ON THE TOTAL CURVATURE OF KNOTS

ON THE TOTAL CURVATURE OF KNOTS

2'n, equality holding only for plane convex curves. K. Borsuk, in 1947, extended this result to n dimensional space, and, in the same paper, conjectured that the total curvature of a knot in three dimensional space must exceed 47r. A proof of this conjecture is presented below.' In proving this proposition, use will be made of a definition, suggested by R. H. Fox, of total curvature which is applicable to any closed curve. This general definition is validated by showing that the generalized total curvature K(C) is

John Milnor | J. Milnor

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[3] E. Artin,et al. Some Wild Cells and Spheres in Three-Dimensional Space , 1948 .

[4] István Fáry. Sur la courbure totale d'une courbe gauche faisant un nœud , 1949 .