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arXiv · 1504.03748

Minimal helix submanifolds and Minimal Riemannian foliations

Antonio J. Di Scala·Gabriel Ruiz-Hernandez
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Abstract

We investigate minimal helix submanifolds of any dimension and codimension immersed in Euclidean space. Our main result proves that a ruled minimal helix submanifold is a cylinder. As an application we classify complex helix submanifolds of $\mathbb{C}^n$: They are extrinsic products with a complex line as a factor. The key tool is Corollary 1.3 which allows us to classify Riemannian foliations of open subsets of the Euclidean space with minimal leaves. Finally, we consider the case of a helix hypersurface with constant mean curvature and prove that it is either a cylinder or an open part of a hyperplane.

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Antonio J. Di Scala, Gabriel Ruiz-Hernandez. 2015-04-15. Minimal helix submanifolds and Minimal Riemannian foliations. https://arxiv.org/abs/1504.03748

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