Transformations of Einstein spaces
- Creators
- Robertson, H. P.
Abstract
In a paper which is to be published elsewhere are obtained all Einstein manifolds whose line elements are determined by a quadratic differential form of the type ds^2 = f(xyzt)(dx^2 + dy^2 + dz^2) + g(xyzt)dt^2 (1) where f is really a function of t. Of the ten apparently distinct solutions of the cosmological equations for an element of this type one represents a hypersphere,(1) two are characterized by the fact-that f and g involve an essentially complex argument and in the remaining seven, f is in each case related to a Weierstrass p-function. This suggests that only three of the ten solutions are distinct and that the relations between the various solutions of each group are to be found by transformation of coordinates. It is the purpose of this note to develop a theorem which will establish these relations.
Additional Information
© 1925 by the National Academy of Sciences. Communicated August 19, 1925. [H.P.R. was a] National Research Fellow in Mathematics.Attached Files
Published - ROBpnas25.pdf
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Additional details
- PMCID
- PMC1086164
- Eprint ID
- 8577
- Resolver ID
- CaltechAUTHORS:ROBpnas25
- National Research Council
- Created
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2007-08-21Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field