Shape Equations for Two-Dimensional Manifolds through a Moving Frame Variational Approach

Authors

Paul Bracken, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

9-2019

Abstract

A variational approach is given which can be applied to functionals of a general form to determine a corresponding Euler–Lagrange or shape equation. It is the intention to formulate the theory in detail based on a moving frame approach. It is then applied to a functional of a general form which depends on both the mean and Gaussian curvatures as well as the area and volume elements of the manifold. Only the case of a two-dimensional closed manifold is considered. The first variation of the functional is calculated in terms of the variations of the basic variables of the manifold. The results of the first variation allow for the second variation of the functional to be evaluated.

Comments

© 2020 World Scientific Publishing Co Pte Ltd. Original published version available at https://doi.org/10.1142/S021988781950155X

Recommended Citation

Bracken, Paul. 2019. “Shape Equations for Two-Dimensional Manifolds through a Moving Frame Variational Approach.” International Journal of Geometric Methods in Modern Physics 16 (10): 1950155. https://doi.org/10.1142/S021988781950155X.

Publication Title

International Journal of Geometric Methods in Modern Physics

DOI

10.1142/S021988781950155X