Intrinsically defined curves and special functions

Abstract

We study two classes of plane curves with prescribed curvature. First, we investigate spirals whose curvature is a power function, and express coordinates of the spirals' centers in terms of the gamma function.

For curves in the second family, the curvature is a multiple of the sine function. We show that this family contains infinitely many closed curves and provide their characterization in terms of the zeroth order Bessel function.

Keywords

• differential geometry
• curvature
• planar curve
• gamma function
• Bessel function