Since millimeter wave (mmWave) communications have wideband channels, mmWave signal corruptions increase due to radio-channel frequency selectivity. In this case, the combination of the orthogonal frequency division multiplexing (OFDM) with the mmWave MIMO system is envisioned as a candidate technique to address the degradation of communication. As hybrid analog/digital architecture offers potential energy and spectral efficiency for the mmWave MIMO device. Matrix factorization formulation with singular value decomposition (SVD) is the most used method for designing the hybrid precoder/combiner. However, using SVD decomposition in precoding/combining designing requires power allocation schemes due to the different signal-to-noise ratios (SNRs) of different subchannels. To achieve a high wireless communications capacity, we propose in this work an alternating minimization algorithm based on a manifold optimization technique using the geometric mean decomposition (GMD) (called MO-AltMin-GMD) to derive unconstrained optimal precoders and combiners from the channel state information (CSI). The main advantage is that the proposed hybrid design avoids any allocation schemes in order to reduce the hybrid architecture complexity. Numerical simulations show that the proposed hybrid design provides high results compared to the existing methods in terms of spectral efficiency.