The Geometry of the Secant Caustic of a Planar Curve

Abstract

The secant caustic of a planar curve $M$ is the image of the singular set of the secant map of $M$. We analyse the geometrical properties of the secant caustic of a planar curve, i.e. the number of branches of the secant caustic, the parity of the number of cusps and the number of inflexion points in each branch of this set. In particular, we investigate in detail some of the geometrical properties of the secant caustic of a rosette, i.e. a smooth regular oriented closed curve with non-vanishing curvature.

23 pages, 11 figures

References in corpus (5)

• The improved isoperimetric inequality and the Wigner caustic of planar ovals
• Singular points of the Wigner caustic and affine equidistants of planar curves
• The Gauss-Bonnet Theorem for coherent tangent bundles over surfaces with boundary and its applications
• The Constant Width Measure Set, the Spherical Measure Set and isoperimetric equalities for planar ovals
• The Geometry of the Wigner Caustic and a Decomposition of a Curve Into Parallel Arcs

Cited by in corpus (1)

• Singular points of the Wigner caustic and affine equidistants of planar curves