The present paper investigates the flatness of a Riemannian manifold associated with a gen-eralized quarter-symmetric connection transform group (in briefly, GQSC) and confirms some interesting geometrical flatness. In particular, some special Ricci flatness of a manifold with a generalized quarter-symmetric connection homotopy via the projective invariant and the conformal invariant are obtained.
Zhao et al. (Wed,) studied this question.