6533b7dafe1ef96bd126ecee

RESEARCH PRODUCT

The geometry of the secant caustic of a planar curve

Wojciech DomitrzM. C. Romero FusterM. Zwierzyński

subject

Mathematics - Differential GeometryPlanar curveMathematics::Commutative AlgebraAstrophysics::High Energy Astrophysical PhenomenaMathematics::History and OverviewGeometryCurvatureImage (mathematics)Mathematics::Algebraic GeometryDifferential Geometry (math.DG)Computational Theory and MathematicsFOS: MathematicsAstrophysics::Earth and Planetary AstrophysicsGeometry and TopologyCaustic (optics)AnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2018-02-28Differential Geometry and its Applications
https://doi.org/10.1016/j.difgeo.2021.101797