# Scalar curvature and warped-product manifolds - intuition

Let $$(M, g) = (N_1, g_1) \times_f(N_2, g_2)$$ be an Einstein warped-product manifold, with metric $$g=g_1+f^2g_2$$.

What does it mean if the scalar curvature of its base-manifold $$(N_1, g_1)$$, equal to a multiple of the $$f$$ warping function?

Does it has any geometrical or physical meaning?