Page:BatemanConformal.djvu/4

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1908.]
78
The conformal transformations of a space of four dimensions.

First, let V be a homogeneous function of degree zero. We evidently have

But, since V is a homogeneous function of degree zero,

and ν = -1, therefore

If, instead of (l, m, n, λ, μ, ν), we use the usual hexaspherical coordinates defined by the relations

;

the equation takes the more symmetrical form

This relation shows that a homogeneous function of degree zero, which is a solution of

i.e., of