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Context. Stellar internal magnetic fields have recently been shown to leave adetectable signature on period spacing patterns of gravity modes.  Aims. We investigate the effect of the obliquity of a mixed (poloidal andtoroidal) dipolar internal fossil magnetic field with respect to the rotationaxis on the frequency of gravity modes in rapidly rotating stars.  Methods. We use the traditional approximation of rotation to computenon-magnetic modes, and a perturbative treatment of the magnetic field tocompute the corresponding frequency shifts. We apply the new formalism to HD43317, a magnetic, rapidly rotating, slowly pulsating B-type star, whose fieldhas an obliquity angle of about 80{\deg}.  Results. We find that frequency shifts induced by the magnetic field onhigh-radial-order gravity modes are larger with increasing obliquity angle,when the magnetic axis is closer to the equatorial region, where these modesare trapped. The maximum value is reached for an obliquity angle of 90{\deg}.This trend is observed for all mode geometries.  Conclusions. Our results predict that the signature of an internal obliquedipolar magnetic field is detectable using asteroseismology of gravity modes.

Period spacings of gravity modes in rapidly rotating magnetic stars II. The case of an oblique dipolar fossil magnetic field