  Let $\Sigma^n$ be a compact, embedded, oriented hypersurface in a compact
oriented Riemannian manifold $N^{n+1}$ with the second fundamental form $h$.
Let $H={\rm tr}_{g_{\Sigma}} h$ and $S=|h|^2$ be the mean curvature and squared
length of the second fundamental form $h$ of $\Sigma$, respectively. If the
Ricci curvature of $N^{}$ is bounded from below by a positive constant $k>0$
and the sectional curvature of $N^{}$ is bounded from above by a positive
constant $K>0$, then the first nonzero eigenvalue of the Laplacian on $\Sigma$
has a lower bound
  $$\lambda_1(\Sigma)\geq
  \frac {k}{2}-
  \frac{H_{\Sigma}}{2}
  \left(
  nK+\frac{2\sqrt{S_{\Sigma}K}}{\arctan(\sqrt{K})}+2n\sqrt{S_{\Sigma}}
+\frac{n}{n+1}H_{\Sigma}
  \right).$$ where $H_{\Sigma}=\max_{\Sigma}|H|$ and
$S_{\Sigma}=\max_{\Sigma}S$. It extends the result of Choi and Wang [J. Diff.
Geom. \textbf{18} (1983), 559--562.] to non-minimal case.
