  In this paper, we study the evolving behaviors of the first eigenvalue of
Laplace-Beltrami operator under the normalized backward Ricci flow, construct
various quantities which are monotonic under the backward Ricci flow and get
upper and lower bounds. We prove that in cases where the backward Ricci flow
converges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue
evolves toward zero.
