On convexity of simple closed frontals

Tomonori Fukunaga, Masatomo Takahashi
2016 Kodai Mathematical Journal  
We study convexity of simple closed frontals in the Euclidean plane by using the curvature of Legendre curves. We show that for a Legendre curve, the simple closed frontal is convex if and only if the sign of both functions of the curvature of the Legendre curve does not change. We also give some examples of convex simple closed frontals. 2010 Mathematics Subject classification: 58K05, 53A04, 57R45
doi:10.2996/kmj/1467830145 fatcat:czd7qgsm3va4xoy4p3pmibvfsq