  There are three types of fragmentation functions (FFs) which are used to
describe the twist-3 cross sections of the hard semi-inclusive processes under
QCD collinear factorization, and they are called intrinsic, kinematical, and
dynamical FFs. In this work, we investigate the theoretical relations among
these FFs for a tensor-polarized spin-1 hadron. Three Lorentz-invariance
relations are derived by using the identities between the nonlocal quark-quark
and quark-gluon-quark operators, which guarantee the frame independence of the
twist-3 spin observables. The QCD equation of motion relations are also
presented for the tensor-polarized FFs. In addition, we show that the intrinsic
and kinematical twist-3 FFs can be decomposed into the contributions of twist-2
FFs and twist-3 three-parton FFs, and the latter are also called dynamical FFs.
If one neglects the dynamical FFs, we can obtain relations which are analogous
to the Wandzura-Wilczek relation. Then, the intrinsic and kinematical twist-3
FFs are expressed in terms of the leading-twist ones. Since the FFs of a spin-1
hadron can be measured at various experimental facilities in the near future,
these theoretical relations will play an important role in the analysis of the
collinear tensor-polarized FFs.
