Tables of Hodge Duals


These are found in the attached note. Table 1’s left hand column gives six examples of a commutator acting on a vector to give curvature and torsion tensors. The right hand column gives the six entries of the left hand column after Hodge dual transformation and index lowering for each entry. it is seen that the six entries on the right hand side are the same as those on the left hand side, they have just been rearranged. So the Hodge dual operation (2) is an example of the original operation (1). This means that if D ^ T := R ^ q then D ^ T tilde := R tilde ^ q These are examples of the Cartan Bianchi identity and Cartan Evans dual identity proven in all detail in many ways in many notes and papers. These proofs are self checking and irrefutable. Any attempt to “refute” them is part of deliberate scientific fraud and should be rejected by the international community. The fraudsters seem on first sight to come from a reputable background, but on scholarly scrutiny by several independent scholars have been found to commit fraud many times and in a systematic, deliberate manner. It is all over for them now because of the long term international acceptance of the correctness of ECE theory (the obvious, self checking, correctness of Cartan geometry within its terms of reference). It is easy to deceive people these days because of the ghastly complexity of standard physics. Often this means nothing at all. There is a maths phobia and I often see senior scientists ducking the mathematics and leaving the field wide open for fraudsters. So I have give 132 papers and a thousand background notes to try to expose this fraud. Other scholars have tried to expose the fraud independently.



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