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Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 17 Issue: 1

Rotational Self-Shrinkers in Euclidean Spaces

Kadri Arslan(Bursa Uludağ Üniversitesi)0000-0002-1440-7050
Yılmaz Aydın0000-0003-4292-5880
Betül Bulca Sokur(Bursa Uludağ Üniversitesi)0000-0001-5861-0184
Sayfa
—
Yayın Tarihi
2024-04-23
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Moreover, we give the necessary and sufficient conditions for these type of submanifolds to be homothetic solitons for their mean curvature flows.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The rotational embedded submanifold of $\mathbb{E}^{n+d}$ first studied by N.
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Temel Bulgular & Veri:The second named authour and at. all recently have considered $3-$dimensional rotational embedded submanifolds in $\mathbb{E}^{5}$.
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Sonuç & Katkı:Moreover, we give the necessary and sufficient conditions for these type of submanifolds to be homothetic solitons for their mean curvature flows.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Rotational submanifold · mean curvature flow · homothetic soliton

Abstract

The rotational embedded submanifold of $\mathbb{E}^{n+d}$ first studied by N. Kuiper. The special examples of this type are generalized Beltrami submanifolds and toroidals submanifold. The second named authour and at. all recently have considered $3-$dimensional rotational embedded submanifolds in $\mathbb{E}^{5}$. They gave some basic curvature properties of this type of submaifolds. Self-similar flows emerge as a special solution to the mean curvature flow that preserves the shape of the evolving submanifold. In this article we consider self-similar submanifolds in Euclidean spaces. We obtained some results related with self-shrinking rotational submanifolds in Euclidean $5-$space $\mathbb{E}^{5}$. Moreover, we give the necessary and sufficient conditions for these type of submanifolds to be homothetic solitons for their mean curvature flows.

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Bu Makaleye Atıf Yap

Arslan, K., Aydın, Y., Sokur, B. B. (2024). Rotational Self-Shrinkers in Euclidean Spaces. International Electronic Journal of Geometry, Volume: 17 Issue: 1. https://doi.org/10.36890/iejg.1330887

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