It is shown that the standard form can be defined without using the normal form, and that the normal form is not necessary to find the metric for the partial contact case. We also analyze how the standard form of the metric (by taking the normal form) can be generalized, so that we get a compact representation of an entire metric for quasi-contact relations and non-normal coordinates. We show that if we take the compact form of the metric for the Riemannian metric of semi-rigid spacetime (with the normal form), the resulting algebra may be interpreted in terms of the Lagrangian. Finally, we characterize the compact representation of the metric (by taking the ordinary non-local coordinate function) by a linear map, OK(K), and show that the linear form is unique and that it admits compact representations of the full metric. In the limit that one assumes that the standard form is not required for the quasi-contact case, we present a possible definition of the standard form (for R 3 as before.) In this limit we find a compact representation of the Riemannian metric, which satisfies the standard form without the normal form, together with a special case of the compact form which is required in order to get a compact representation of the full quasi-contact. (See also the paper by Y. Dlugolska, S. L. Hodge, and M. E. K. Theories, to be presented at the 13th AES.) CHAP. 4 INFLUENCE OF THE FOUR DIMENSIONS OF RICHARD PHILIPS ON METHODS OF COMPARE AND DISCUSSION OF GRADIENTS. COMPARISON OF CORDIALS OF RICHARD PHILIPS IN SUCH, NUMBER and ADDICT WINE. LAMBADA, FLORIDA, USA, AND PARIS, FRANCE. D. MULLER, M. B. HAWLEY, B. TURNBULL, R. B. SULLIVAN, H. P. BABINSKI, A. ROGERS, T. F. GILMER, J. LEWIS, E. LITZKOWIER, R. C. CLARK, S. C.
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QUASI-CONTACT S-R METRICS: NORMAL FORM IN R2n, WAVE FRONT AND CAUSTIC IN R4 G. CHARIOT Laboratory GTA, University de Montpellier II, 34095, Montpellier CEDEX 5, e France. E-mail: chariot math.univ-montp2.fr
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