Affiliation:
1. Department of Mathematics , Hiroshima University , Higashi-Hiroshima 739-8526, Hiroshima , Japan
Abstract
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.
Funder
Japan Society for the Promotion of Science
Subject
Applied Mathematics,General Mathematics