A covariantly constant dynamical two-form is exploited on a $D_3$-brane to
obtain its gravity dual action, governing an $S^3$ deformed $AdS_5$ black hole,
in a type IIB string theory on $S^1\times K3$. We invoke the Kaluza-Klein
compactification to work out the open/closed string duality. Interestingly, the
Reissner-Nordstrom black hole is obtained on the "non-Reimannian" braneworld.