Rotational Self-Shrinkers in Euclidean Spaces

Authors : Kadri Arslan, Yılmaz Aydın, Betül Bulca Sokur

Pages : 34-43

Doi:10.36890/iejg.1330887

View : 62 | Download : 79

Publication Date : 2024-04-23

Article Type : Research Paper

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.
Keywords : Rotational submanifold, mean curvature flow, homothetic soliton, self shrinkers