Self-shrinker Type Submanifolds in the Euclidean Space

Guan, Zhanyu; Li, Fengjiang

doi:10.1007/s41980-020-00369-7

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Rotational Self-shrinkers In Euclidean Spaces1

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2024

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“…The case of vanishing λ is the well-known case of minimal submanifold, which of course is stationary under the action of the flow [17]. Infact, self-similar submanifolds are spacial type of self-shrinker submanifolds with λ = 1 [20].…”

Section: Rotational Self-shrinkers In Euclidean Spacesmentioning

confidence: 99%

Rotational Self-Shrinkers in Euclidean Spaces

Arslan,

Aydın,

Bulca Sokur

2024

International Electronic Journal of Geometry

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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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Section: Rotational Self-shrinkers In Euclidean Spacesmentioning

confidence: 99%