By John Henry Constantine Whitehead

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716-725. Immediately preceding this, O. Veblen (Journal of the London Mathematical Society, vol. 4 (1929), pp. 140-160) had dealt with projective displacement from a different point of view. He showed how the space of projective vectors at any point, which plays the part of the associated space, is related to the space of differentials. X Mathematische Annalen, vol. 99 (1928), pp. 413-434. § L. P. Eisenhart, Non-Riemannian Geometry, p. 47. These scalars are given by a a % j where the semi-colon denotes covariant differentiation with respect to the affine connection, and are the contra variant vectors of the w-uple.

Eisenhart, Non-Riemannian Geometry, p. 47. These scalars are given by a a % j where the semi-colon denotes covariant differentiation with respect to the affine connection, and are the contra variant vectors of the w-uple. In his treatment of non-holonomic affine spaces 2 a Cartan (Annales de l'Ecole Normale Supgrieure, 1923) uses « -f n Pfaffian forms, u> and up. The former give the coordinates of a point in each tangent space, and the latter define the affine connection. 2) these forms are given by || Annals of Mathematics, vol.

Z", such that = «2 for x a a = q. 3) From the condition Jl% = 5jJ we have 1 were (F (x) depend only on x , ... in the representation given by n x. 5) it follows that Z* = 5£ and a 52 for x = a q. 5). It follows that Pjk - 0. 1). 3) we may change to any m representation, provided we know its relation to x + x°. W e shall start with the representation y + y°, where y° = x° — q°, and y* are affine normal coordinates for n # , the point qt and the coordinate system x. a a For x = q we have, therefore, y a = 0, Let n j T be the components of ir in y + y°.