Handover (HO) management is one of the most crucial tasks in dense cellular networks with mobile users. A problem in the HO management is to deal with increasing HOs due to network densification in the 5G evolution and various HO skipping techniques have so far been studied in the literature to suppress excessive HOs. In this paper, we propose yet another HO skipping scheme, called periodic HO skipping. The proposed scheme prohibits the HOs of a mobile user equipment (UE) for a certain period of time, referred to as skipping period, thereby enabling flexible operation of the HO skipping by adjusting the length of the skipping period. We investigate the performance of the proposed scheme on the basis of stochastic geometry. Specifically, we derive analytical expressions of two performance metrics -- the HO rate and the expected downlink data rate -- when a UE adopts the periodic HO skipping. Numerical results based on the analysis demonstrate that the periodic HO skipping scenario can outperform the scenario without any HO skipping in terms of a certain utility metric representing the trade-off between the HO rate and the expected downlink data rate, in particular when the UE moves fast. Furthermore, we numerically show that there can exist an optimal length of the skipping period, which locally maximizes the utility metric, and approximately provide the optimal skipping period in a simple form. Numerical comparison with some other HO skipping techniques is also conducted.