This result states eells-sampson theorem: given (M,g) be a closed smooth Riemannian manifold, and let (N,h) be a compact smooth Riemannian manifold whose sectional curvature satisfies K N( ) 0 for every 2-plane T qN and.... It is useful in harmonic map theory and elliptic regularity, where variational identities, curvature estimates, and compactness arguments control geometric objects.