Caustics of pseudo-spherical surfaces in the Euclidean 3-space-Reference-Cited by-同舟云学术

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

Published:2023-06-27 Issue:1 Volume:36 Page:21-32
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Teramoto Keisuke¹^ORCID

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

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2022-0345/pdf

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