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 the complex Euclidean space: 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.
|Titolo:||Minimal helix submanifolds and minimal Riemannian foliations|
|Data di pubblicazione:||2016|
|Digital Object Identifier (DOI):||10.1007/s40590-015-0074-6|
|Appare nelle tipologie:||1.1 Articolo in rivista|