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Journals / International Electronic Journal of Geometry / 2016 / Cilt: 9 - Sayı: 2

Differential Geometry of Rectifying Submanifolds Bang-Yen Chen (Communicated by Kazım ?Ilarslan)

Bang-Yen CHEN
Pages
1–8
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

Moreover, rectifying submanifolds with arbitrary codimensionare completely determined.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A space curve in a Euclidean 3-space E3is called a rectifying curve if its position vector fieldalways lies in its rectifying plane.
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Key Findings & Data:Monthly 110 (2003), no. 2, 147-152].
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Conclusion & Impact:Moreover, rectifying submanifolds with arbitrary codimensionare completely determined.
🔬Design:Research Article
📍Scope:2003 Verileri
⚙️Variables:Domain Parameters

Abstract

A space curve in a Euclidean 3-space E3is called a rectifying curve if its position vector fieldalways lies in its rectifying plane. This notion of rectifying curves was introduced by the authorin [Amer. Math. Monthly 110 (2003), no. 2, 147-152]. In this present article, we introduce andstudy the notion of rectifying submanifolds in Euclidean spaces. In particular, we prove that aEuclidean submanifold is rectifying if and only if the tangential component of its position vectorfield is a concurrent vector field. Moreover, rectifying submanifolds with arbitrary codimensionare completely determined.

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Cite This Article

CHEN, B. (2022). Differential Geometry of Rectifying Submanifolds Bang-Yen Chen (Communicated by Kazım ?Ilarslan). International Electronic Journal of Geometry, Cilt: 9 - Sayı: 2, 1–8. https://ajindex.com/articles/539711

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