Recent Results on $\psi(3770)$ Physics at BES-II

About 33, 6.5 and 1.0 pb$^{-1}$ of $e^+e^-$ annihilation data were, respectively, taken around the center-of-mass energies of $\sqrt s=$ 3.773 GeV, at $\sqrt s=$ 3.650 GeV and at $\sqrt s=$ 3.6648 GeV with the BES-II detector at the BEPC collider. By analyzing these data sets, we measure the branching fraction for $\psi(3770)\to$ non-$D\bar D$; observe an anomalous line shape of the cross section for $e^+e^-\to$ hadrons in the energy region from 3.650 to 3.872 GeV; and measure the line shapes of the $D^+D^-$, $D^0\bar D^0$ and $D\bar D$ production and the ratios of the production rates of $D^+D^-$ and $D^0\bar D^0$ in $e^+e^-$ annihilation at $\psi(3770)$ resonance. We also search for $\psi(3770)$ decay into exclusive light hadron processes containing $K^0_S$ or $\pi^0\pi^0$ mesons in the final states.