Most of the planetary nebulae (PN) have bipolar or other non-spherically symmetric shapes. The presence of a magnetic field in the central star may be the reason for this lack of symmetry, but observational works published in the literature have so far reported contradictory results. We try to correlate the presence of a magnetic field with the departures from the spherical geometry of the envelopes of planetary nebulae. We determine the magnetic field from spectropolarimetric observations of ten central stars of planetary nebulae. The results of the analysis of the observations of four stars was previously presented and discussed in the literature, while the observations of six stars, plus additional measurements for a star previously observed, are presented here for the first time. All our determinations of magnetic field in the central planetary nebulae are consistent with null results. Our field measurements have a typical error bar of 150-300 G. Previous spurious field detections obtained with FORS were probably due to the use of different wavelength calibration solutions for frames obtained at different position angles of the retarder waveplate. Currently, there is no observational evidence for the presence of magnetic fields with a strength of the order of hundreds Gauss or higher in the central stars of planetary nebulae.
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