Abstract
In this paper, we consider an n-dimensional compact Riemannian manifold (M,g) of constant scalar curvature and show that the presence of a non-Killing conformal vector field ξ on M that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue λ together with a condition on Ricci curvature of M, that the Ricci curvature in the direction of a certain vector field is greater than or equal to (n − 1)λ, forces M to be isometric to the n-sphere Sn(λ).
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