Geometric characteristics of a manifold associated with a GQSC transform group

Abstract

The present paper  investigates the flatness of a Riemannian manifold associated with a generalized 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.