Equations for 16-component vector-bispinor field, originated from Rarita-Schwinger Lagrangian for spin 3/2 field extended to Riemannian space-time are investigated. Additional general covariant constrains for the field are produced, which for some space-time models greatly simplify original wave equation. Peculiarities in description of the massless spin 3/2 field are specified. In the flat Minkowski space for massless case there exist gauge invariance of the main wave equation, which reduces to possibility to produce a whole class of trivial solutions in the the form of 4-gradient of arbitrary (gauge) bispinor function, \Psi ^{ 0}_{ c} = \partial_{ c} \psi. Generalization of that property for Riemannian model is performed; it is shown that in general covariant case solutions of the gradient type \Psi^{ 0}_{ \beta} = (\nabla_{ \beta} + \Gamma_{ \beta})\Psi exist in space-time regions where the Ricci tensor obeys an identity R_{ \alpha \beta} - { 1 \over 2} R g_{ \alpha \beta} = 0.
Categories: math-ph math.MP