1. Unpublished. There are close similarities to the work on general (or «curvilinear») projective geometry bySchouten and others of the «Dutch school» in the thirties.
2. LettingV σ be an independent field seems to lead to anomalous, unphysical terms in the field equations derived in sect.2.
3. This result, in fact the whole introduction of the frame (ã), culminating in the decomposed form (2.19) of the field equations, is familiar from the projective relativity of Veblen and Hoffmann (O. Veblen andB. Hoffmann:Phys. Rev.,36, 810 (1930)) and formally goes back to earlier work byKaluza. Of course, in spite of these formal similarities, from our point of view that work was physically wrong since the spaces were wrong and the groups too big (did not preserve space-time angle or even length!). Nevertheless,Kaluza was the first to see correctly how to unify a skew field like the EM force tensor with a symmetric metric tensor.
4. SeeL. P. Eisenhart:Riemannian Geometry (Princeton, N. J., 1926), formula (28.5).
5. Cf., say,R. Adler, M. Bazin andM. Schiffer:Introduction to General Relativity, 2nd ed., eq. (10.101a) (New York, N. Y., 1975). In spite of the difference of metric, it is true that ourR μν andG μν are the same asR μν (ABS) andG μν (ABS) . Moreover, our convention on the sign ofT μν , namelyT 44≥0, agrees with theirs. Recall our natural units: ħ=c=1.