On a complete noncompact K¨ahler manifold we prove that the bottom of the spectrum for the Laplacian is bounded from above
by m2 if the Ricci curvature is bounded from below by −2(m+1). Then we show that if this upper bound is achieved then either the
manifold is connected at infinity or it has two ends and in this case it is diffeomorphic to the product of the real line with a compact
manifold and we determine the metric.