Work

Discrete curve theory in space forms: planar elastic and area-constrained elastic curves

Year: 2025

Type: article

Abstract: We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equation to space forms and reflects various geometric properties known from their smooth counterparts. Special emphasis is paid to discrete flows built from Bäcklund transformations in the respective space forms. The invariants of the flows form a hierarchy of curves and we show that discrete elastic and constrained elastic curves can be characterized as elements of this hierarchy. This work also includes an introductory chapter on discrete curve theory in space forms, where we find discrete Frenet-type formulas and describe an associated family related to a fundamental theorem.

Source: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

DOI: 10.1007/s13366-025-00817-7

Authors: Tim Hoffmann, Jannik Steinmeier, Gudrun Szewieczek

Institutions: Technical University of Munich, Universität Innsbruck

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Deutsche Forschungsgemeinschaft, Medizinische Universität Innsbruck, Universität Innsbruck