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• Of course in almost all geometric theories of gravity metric is the fundamental field, especially in General Relativity.
• Although we have used the term pseudo-Riemannain in the abstract and in the introduction, we go against this usage with the same lines of thought as R. Toretti [13], and instead we prefer to use Riemannian spacetime generally and especially Lorentzian spacetime for manifolds endowed with one time-like direction in a local g-frame.
• We use the term Yano form to indicate a KY form or a CCKY form, then the term dual Yano form indicates a CCKY form or a KY form respectively.
• Confusion with the Riemann curvature R tensor should be avoided.
• The properties associated to these projectors are given at the Appendix A of [1].