Abstract
of degree m. Let k (? n) be the minimum number of variables such that the form (1) is expressible in terms of these k variables and their differentials. We shall call the number k the class of the tensor Ai1I2. . i2aTo determine the class of the tensor Ai1 2* *s, let us first inquire under what conditions the form (1) may be expressed in terms of less than n variables and their differentials. This amounts to determining under what conditions there exists a coordinate system K, with reference to which the form (1) is independent of the variable xn and the differentials of xn. With reference to such a coordinate system, the components of the * im must satisfy the conditions
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