Work

On the Focal Geometry of Translation Surfaces: Flatness, Minimality, and Classification Results

Year: 2025

Type: article

Abstract: In this study, we investigate the focal surfaces associated with translation surfaces in Euclidean 3-space from the viewpoint of differential geometry. We begin by defining the translation surface generated by two planar curves and derive the corresponding focal surfaces using the framework of the Frenet frame. Analytical conditions are obtained under which the focal surfaces exhibit minimality or flatness. Several theorems are proven to classify the focal images, supported by illustrative examples. The results provide insights into the curvature structure of translation surfaces and contribute to the broader understanding of their geometric behavior.

Source: Axioms

DOI: 10.3390/axioms14120919

Authors: Sezgin Büyükkütük, İlim Kişi, Günay Öztürk, Emre Kişi

Institutions: Kocaeli Üniversitesi, İzmir Demokrasi Üniversitesi, Sakarya University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

OpenAlex ID: W4417359395

FWCI: 0.484

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Cited by: 1

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