Abstract. A wide variety of interactions take place between the magnetized solar wind plasma outflow from the Sun and celestial bodies within the solar system. Magnetized planets form magnetospheres in the solar wind, with the planetary field creating an obstacle in the flow. The reconnection efficiency of the solar-wind-magnetized planet interaction depends on the conditions in the magnetized plasma flow passing the planet. When the reconnection efficiency is very low, the interplanetary magnetic field (IMF) does not penetrate the magnetosphere, a condition that has been widely discussed in the recent literature for the case of Saturn. In the present paper, we study this issue for Saturn using Cassini magnetometer data, images of Saturn's ultraviolet aurora obtained by the HST, and the paraboloid model of Saturn's magnetospheric magnetic field. Two models are considered: first, an open model in which the IMF penetrates the magnetosphere, and second, a partially closed model in which field lines from the ionosphere go to the distant tail and interact with the solar wind at its end. We conclude that the open model is preferable, which is more obvious for southward IMF. For northward IMF, the model calculations do not allow us to reach definite conclusions. However, analysis of the observations available in the literature provides evidence in favor of the open model in this case too. The difference in magnetospheric structure for these two IMF orientations is due to the fact that the reconnection topology and location depend on the relative orientation of the IMF vector and the planetary dipole magnetic moment. When these vectors are parallel, two-dimensional reconnection occurs at the low-latitude neutral line. When they are antiparallel, three-dimensional reconnection takes place in the cusp regions. Different magnetospheric topologies determine different mapping of the open-closed boundary in the ionosphere, which can be considered as a proxy for the poleward edge of the auroral oval.