We show that the Ricci flat Calabi's metrics on holomorphic line bundles over compact Kähler--Einstein manifolds are not projectively induced. As a byproduct we solve conjecture addressed in [10] by proving any multiple of Eguchi-Hanson metric blow-up $\mathbb{C}^2$ at origin is

The paper aims to investigate curvature inheritance (CI) symmetry in M-projectively flat spacetimes. It is shown that the CI spacetime a conformal motion. We have proved M-projective tensor follows property along vector field ξ, when admits conditions of both and motion or ξ. Also, we derived some results for with perfect fluid following Einstein equations (EFEs) cosmological term admitting an ...