The paper presents a theoretical study of the disturbed isobaric surface shape in the geostrophic state of the atmosphere. It has been shown that depending on the overheat sign at the equator the isobaric surface has the shape of an oblate or prolate geoid. If the geostrophic wind velocity is nonzero at the poles, the local pressure extrema (minima for oblate geoid and maxima for prolate geoid) appear at the poles in the geostrophic state. This result correlates with the well-known polar vortex phenomenon and possibly can refine our understanding and interpretation of the phenomenon. In other words, the existence of polar minima and maxima of the pressure field can be the peculiarity of the geostrophic state of the atmosphere. It has been found that air must be colder than surrounding atmosphere for initiation of the zonal eastward transport. For warm air mass only easterly winds will be observed.