  We analyze virtual Compton scattering off the nucleon at low energies in a
covariant, model-independent formalism.
  We define a set of invariant functions which, once the irregular nucleon pole
terms have been subtracted in a gauge-invariant fashion, is free of poles and
kinematical zeros.
  The covariant treatment naturally allows one to implement the constraints due
to Lorentz and gauge invariance, crossing symmetry, and the discrete
symmetries.
  In particular, when applied to the $ep\to e'p'\gamma$ reaction,
charge-conjugation symmetry in combination with nucleon crossing generates four
relations among the ten originally proposed generalized polarizabilities of the
nucleon.
