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A decomposition identity for a class of Riemannian invariants†

Published online by Cambridge University Press:  24 October 2008

Richard Pavelle
Richard Pavelle
Affiliation:
Department of Mathematics, The University of Arizona, Tucson, Arizona 85721
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Abstract

An identity of fundamental interest in General Relativity is the breakup or ‘decomposition’ of the scalar curvature density into an ordinary divergence in addition to a term constructed solely from the metric tensor and its first derivative. It is proven that this identity is the most elementary example of an identity satisfied by all members of a particularly important class of Riemannian invariants. For a subset of these invariants, the decomposition identity undergoes a simplification that connects this material with some problems of current research interest.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 459 - 463
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

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