We have analyzed the shape of the solar corona using the data of daily observations with Mark-3/4 (1980-2008) and SOHO/Lasco-2 (1996–2008) telescopes. The angles of deviation of coronal rays from the radial direction Δθ vary cyclically, reaching the maximum deviation towards the solar equator at the minimum of the solar activity. At the minimum of the 24-th cycle of activity, the Δθ angles were smaller than they were at the minimum of the 22-nd and 23-rd cycles.

We also analyzed of the solar structure corona during eclipses for minimum activity from 1870 till 2008. We examined changes in the index, which characterizes the angle of large coronal streamers to the equatorial plane. It has been shown that the index has been smoothly changing during the last 140 years. The maximal value of an index was during 17–19 activity cycles. The minimal values are reached in the end of 19 centuries and at the present time.

We consider the relations between the angles of deviation of coronal rays at the minimum of activity, the parameters of the global magnetic field of the Sun, and the amplitude of the subsequent cycle of activity, and discuss the hypothesis that the variations of the inclination of coronal rays may affect the parameters of the solar wind and the indices of geomagnetic perturbations at the minima of the solar activity cycles.