  Let C be a hyperelliptic Riemann surface. We show that the hyperelliptic
Weierstrass points of C are non-degenerated critical points of Morse index +2
of the curvature function K of the Theta metric on C (called also Bergman
metric). When the genus of C is two, we compute all critical points of K and we
show in this case that K is a Morse function.
