Abstract
In this paper, we give some classifications of the k-Yamabe solitons on the hypersurfaces of the Euclidean spaces from the vector field point of view. In several results on k-Yamabe solitons with a concurrent vector field on submanifolds in Riemannian manifolds, is proved that a k-Yamabe soliton (M-n, g, v(T), lambda) on a hypersurface in the Euclidean space Rn+1 is contained either in a hypersphere or a hyperplane. We provide an example to support this study and all of the results in this paper can be implemented to Yamabe solitons for k-curvature with k = 1.