Delaunay surfaces expressed in terms of a Cartan moving frame

Authors

Paul Bracken, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2-2020

Abstract

Delaunay surfaces are investigated by using a moving frame approach. These surfaces correspond to surfaces of revolution in the Euclidean three-space. A set of basic one-forms is defined. Moving frame equations can be formulated and studied. Related differential equation which depend on variables relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case in which the mean curvature is constant, these functions can be expressed in terms of Jacobi elliptic functions.

Comments

© 2020 Walter de Gruyter GmbH, Berlin/Boston. Original published version available at https://doi.org/10.1515/jaa-2020-2012

Recommended Citation

Bracken, P. (2020). Delaunay surfaces expressed in terms of a Cartan moving frame, Journal of Applied Analysis, 26(1), 153-160. doi: https://doi.org/10.1515/jaa-2020-2012

First Page

153

Last Page

160

Publication Title

Journal of Applied Analysis

DOI

10.1515/jaa-2020-2012