Page:Eddington A. Space Time and Gravitation. 1920.djvu/220

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204
APPENDIX

Note 4 (p. 81).

The condition for flat space in two dimensions is

.

Note 5 (p. 89).

Let be the determinant of four rows and columns formed with the elements .

Let be the minor of , divided by .

Let the "3-index symbol" {, } denote summed for values of from 1 to 4. There will be 40 different 3-index symbols.

Then the Riemann-Christoffel tensor is , the terms containing being summed for values of from 1 to 4.

The "contracted" Riemann-Christoffel tensor can be reduced to

,

where in accordance with a general convention in this subject, each term containing a suffix twice over ( and ) must be summed for the values 1, 2, 3, 4 of that suffix.

The curvature , summed in accordance with the foregoing convention.

Note 6 (p. 94).

The electric potential due to a charge is ,