  The coexistence of $\pi$-flux state and d-wave RVB state is considered in
this paper within the slave boson approach. A critical value of doping
concentration $\delta_c$ is found, below which the coexisting $\pi$-flux and
d-wave RVB state is favored in energy. The pseudo Fermi surface of spinons and
the physical electron spectral function are calculated. A clear Fermi-level
crossing is found along the (0,0) to ($\pi$, $\pi$) direction, but no such
crossing is detected along the ($\pi$, 0) to ($\pi$, $\pi$) direction. Also, an
energy gap of d-wave symmetry appears at the Fermi level in our calculation.
The above results are in agreement with the angle-resolved photoemission
experiments which indicate at a d-wave pseudo-gap and a half-pocket-like Fermi
surface in underdoped cuprates.
