On the problem of algebraic completeness for the invariants of the Riemanntensor: I

We present a new determining set, CZ, of Riemann invariants which possesses the minimum degree property. From an analysis on the possible independence of CZ, we are led to the division of all space-times into two distinct, in variantly characterized, classes: a general class M-G(+), and a special, si ngular class M-S. For each class, we provide an independent set of invarian ts (I(G)(+)subset of CZ and I(S)subset of CZ, respectively) which, with the results of a sequel paper, will be shown to be algebraically complete. (C) 2001 American Institute of Physics.