INFINITESIMAL CONFORMAL TRANSFORMATIONS OF RIEMANNIAN MANIFOLDS WHICH PRESERVE THE GENERALIZED EINSTEIN TENSOR

摘要

We study conformal transformations leaving the generalized Einstein tensor invariant. We have obtained the system of partial differential equations for the transformations, and explored its integrability conditions. Hence we have got the necessary and sufficient conditions in order that a manifold admit a group of conformal motions, preserving the generalized Einstein tensor. Also we have estimated the number of parameters which the group depends on.