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Rotational self-shrinkers in euclidean spaces

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Arslan, Kadri
Aydın, Yılmaz
Sokur, Betül Bulca

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Int Electronic Journal Geometry

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The rotational embedded submanifolds of E n +d were first studied by N. Kuiper. The special examples of this type are generalized Beltrami submanifolds and toroidals submanifold. The second author and et. all recently have considered 3 - dimensional rotational embedded submanifolds in 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 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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Curvature, Solitons, Flow, Rotational submanifold, Mean curvature flow, Homothetic soliton, Self-shrinkers, Mathematics

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