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XVIII.—The Riemann Tensor in a Completely Harmonic V4

Published online by Cambridge University Press:  14 February 2012

H. S. Ruse
H. S. Ruse
Affiliation:
University College, Southampton
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Extract

If is a fixed point of a Riemannian Vn of fundamental tensor gij, and if s is the geodesic distance between it and a variable point (xi), then the Vn has been called centrally harmonic with respect to the base-point if

is a function of s only, and completely harmonic if this holds for every choice of base-point . A flat Vn (gij=δij) is obviously completely harmonic, since for such a space and

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 62 , Issue 2 , 1946 , pp. 156 - 163
Copyright
Copyright © Royal Society of Edinburgh 1946

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References

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