Scalar curvature and warped-product manifolds - intuition

Question

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?

This post imported from StackExchange MathOverflow at 2018-06-19 08:57 (UTC), posted by SE-user Alexander Pigazzini