Integral Submanifolds in Three-Sasakian Manifolds Whose Mean Curvature Vector Fields are Eigenvectors of the Laplace Operator

Abstract

We find the Legendre curves and a class of integral surfaces in a 7-dimensional three-Sasakian manifold whose mean curvature vectors are eigenvectors of the Laplacian or the normal Laplacian and we give the ex- plicit expression for such surfaces in the sphere $\mathbb{S}^{7}$.