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This investigation reveals geometrical flatness and Ricci flatness in a Riemannian manifold, indicating significant geometric properties.
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.
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Zhao et al. (2025) studied this question.
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