  We show that the five-dimensional general relativity with a negative
cosmological constant allows the solutions of the form M_3 \times M_g where M_3
is the three-dimensional BTZ black hole and M_g is a higher genus (g>1) Riemann
surface with a fixed size. It is shown that this type of spontaneous
compactification on a Riemann surface is possible only for the genus larger
than one. From type IIB string theory point of view, certain near horizon
geometry of D three-branes wrapped on the compact Riemann surface (g>1) is the
BTZ (or AdS_3) space-time tensored with the Riemann surface and a constant size
five-sphere. The relevance of our analysis to the positive energy conjecture of
Horowitz and Myers is discussed.
