We analyze a four-dimensional induced Einstein-Kalb-Ramond theory with a conformally coupled Kalb-Ramond action. We also comment on an Ansatz which is inconsistent with the assumption of maximal form invariance imposed on the Kalb-Ramond field due to the cosmological principle. It is argued that the spatial dependences of various fields considered here are inconsistent with the Friedmann-Robertson-Walker metric. One hence justifies the Ansatz used in many articles. We also show that the contribution from the Kalb-Ramond action is negligible effectively after the inflationary era. Some of the solutions to the field equations are presented.