Associated Families of Surfaces in Warped Products and Homogeneous Spaces
Associated Families of Surfaces in Warped Products and Homogeneous Spaces
We classify Riemannian surfaces admitting associated families in three dimensional homogeneous spaces with four-dimensional isometry groups and in a wide family of (semi-Riemannian) warped products, with an extra natural condition (namely, rotating structure vector field). We prove that, provided the surface is not totally umbilical, such families exist in both …