Abstract
The rotation number of a planar closed curve is the total curvature divided by 2π. This is a regular homotopy invariant of the curve. We shall generalize the rotation number to a curve on a closed surface using conformal geometry of ambient surface. This conformal rotational number is not integral in general. We shall show the fractional part is relevant to harmonic 1-forms of the surface.
Citation
Osamu Kobayashi. "The conformal rotation number." Kodai Math. J. 38 (1) 166 - 171, March 2015. https://doi.org/10.2996/kmj/1426684448
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