Caustics of pseudo-spherical surfaces in the Euclidean 3-space

Abstract

We study geometric properties of caustics of pseudo-spherical surfaces, that is, surfaces with constant negative Gaussian curvature -1 in the Euclidean 3-space ℝ 3 {\mathbb{R}^{3}} . We investigate the Gaussian and the mean curvature of caustics of pseudo-spherical surfaces. Moreover, a certain condition required for the caustics to be minimal surfaces is derived.