Rotational λ−hypersurfaces in euclidean spaces

Abstract

Self-similar flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, λ−hypersurfaces are the generalization of self-similar hypersurfaces. In the present article we consider λ−hypersurfaces in Euclidean spaces which are the generalization of self-shrinkers. We obtained some results related with rotational hypersurfaces in Euclidean 4−space R4 to become self-shrinkers. Furthermore, we classify the general rotational λ−hypersurfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational λ−hypersurfaces in R4.