  The curvature of a magnetic membrane was presented as a means of inducing
nonreciprocities in the spin-wave (SW) dispersion relation (see [Ot\'alora et
al. Phys. Rev. Lett., 2016 117, 227203] and [Ot\'alora et al. Phys. Rev. B.,
2017 95, 184415]), thereby expanding the toolbox for controlling SWs. In this
paper, we further complement this toolbox by analytically showing that the
membrane curvature is also manifested in the absorption of SWs, leading to a
difference in the frequency linewidth (or lifetime) of counterpropagating
magnons. Herein, we studied the nanotubular case, predicting changes of
approximately greater than 10% and up to 20% in the frequency linewidth of
counterpropagating SWs for a wide range of nanotube radii ranging from 30 nm to
260 nm and with a thickness of 10 nm. These percentages are comparable to those
that can be extracted from experiments on heavy metal/magnetic metal
sandwiches, wherein linewidth asymmetry results from an interfacial
Dzyaloshinskii-Moriya interaction (DMI). We also show that the interplay
between the frequency linewidth and group velocity leads to asymmetries in the
SW decay length, presenting changes between 10\% and 22\% for
counterpropagating SWs in the frequency range of 2 - 10 GHz. For the case of
the SW dispersion relation, the predicted effects are identified as the
classical dipole-dipole interaction, and the analytical expression of the
frequency linewidth has the same mathematical form as in thin films with the
DMI. Furthermore, we present limiting cases of a tubular geometry with
negligible curvature such that our analytical model converges to the case of a
planar thin film known from the literature. Our findings represent a step
forward toward the realization of three-dimensional curvilinear magnonic
devices.
