  This work has as the main aim to explore the nature of the fermionic fields,
through a classification of spinor fields about physical space of interest,
such as the bulk and the compactified space $S^7$ from the supergravity
theories. This classification has an extreme utility in the exploration and in
the search for new type of particles, whose observables correspond to bilinear
covariants. In this way, these fields are classified into classes, through
constraints obtained by means of the Fierz-Pauli-Kofink identities and the
bilinear symmetries. We found the Lagrangian terms for the free spinor fields
on spaces of seven compactified dimension in supergravity and, as application
of our spinor fields classification on the bulk, we associate the invariants on
axisymmetric black holes to the components of the bilinear covariants of the
correspondent fermionic field. Besides, we found that a type of spinor
denominated flag-dipole does not generate a brane, but degenerate itself in
other type of spinor called dipole and, in compactification theories, we
obtained the expression to the quantum field on compactified spaces for low
energies in terms of creation and annihilation operators.
