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Journals / Fundamental Journal of Mathematics and Applications / 2023 / Cilt: 6 Sayı: 3

Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three

Büşra SANCI
Fırat YERLİKAYA
Pages
157–169
Publication Date
2023-09-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, we support them with examples.

📌 3 Key Takeaways

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Objective & Hypothesis:In this work, we consider the problem of finding explicit parametrizations for non-degenerate helicoidal surfaces with prescribed curvatures in some conformally flat pseudo-spaces with conformal pseudo-metrics whose conformal factors are related to three types of generic cylindrical functions.
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Key Findings & Data:In the first two, we get a two-parameter family of these surfaces with prescribed extrinsic curvature or mean curvature given by smooth functions.
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Conclusion & Impact:Also, we support them with examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Helicoidal surface · extrinsic curvature · conformally flat pseudo-space

Abstract

In this work, we consider the problem of finding explicit parametrizations for non-degenerate helicoidal surfaces with prescribed curvatures in some conformally flat pseudo-spaces with conformal pseudo-metrics whose conformal factors are related to three types of generic cylindrical functions. In the first two, we get a two-parameter family of these surfaces with prescribed extrinsic curvature or mean curvature given by smooth functions. In the last one, we discover a one-parameter family when both curvatures of these surfaces are zero; however, we find a two-parameter family when either one of those curvatures is zero. Also, we support them with examples.

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Cite This Article

SANCI, B., YERLİKAYA, F. (2023). Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three. Fundamental Journal of Mathematics and Applications, Cilt: 6 Sayı: 3, 157–169. https://ajindex.com/articles/964188

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References (8)

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