We study surfaces in R4 whose tangent spaces have constant principal angles with respect to a plane. Using a PDE we prove the existence of surfaces with arbitrary constant principal angles. The existence of such surfaces turns out to be equivalent to the existence of a special local symplectomorphism of $\R^2$. We classify all surfaces with one principal angle equal to $0$ and observe that they can be constructed as the union of normal holonomy tubes. We also classify the complete constant angles surfaces in R4 with respect to a plane. They turn out to be extrinsic products. We characterize which surfaces with constant principal angles are compositions in the sense of Dajczer-Do Carmo. Finally, we classify surfaces with constant principal angles contained in a sphere and those with parallel mean curvature vector field.
|Titolo:||Surfaces in R4 with constant principal angles with respect to a plane|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||10.1007/s10711-012-9721-5|
|Appare nelle tipologie:||1.1 Articolo in rivista|