In this letter a low-drift monocular SLAM method is proposed targeting indoor scenarios, where monocular SLAM often fails due to the lack of textured surfaces. Our approach decouples rotation and translation estimation of the tracking process to reduce the long-term drift in indoor environments. In order to take full advantage of the available geometric information in the scene, surface normals are predicted by a convolutional neural network from each input RGB image in real-time. First, a drift-free rotation is estimated based on lines and surface normals using spherical mean-shift clustering, leveraging the weak Manhattan World assumption. Then translation is computed from point and line features. Finally, the estimated poses are refined with a map-to-frame optimization strategy. The proposed method outperforms the state of the art on common SLAM benchmarks such as ICL-NUIM and TUM RGB-D.