On geodesic envelopes and caustics

Gianmarco Capitanio (1)

1 IMJ - Institut de Mathématiques de Jussieu

We give a global description of the envelope of the geodesics tangent to a smooth curve in a Riemannian surface. We prove that the envelope is the union of the curve, its inflectional geodesics and its caustic.

Mots clés: Caustics; Envelope theory; Geodesics; Caustics.

Domaines: Géométrie différentielle [math.DG]

Gianmarco Capitanio. On geodesic envelopes and caustics. 2004. ⟨hal-00003326v1⟩