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Transformations of Einstein spaces

Robertson, H. P. (1925) Transformations of Einstein spaces. Proceedings of the National Academy of Sciences of the United States of America, 11 (10). pp. 590-592. ISSN 0027-8424. http://resolver.caltech.edu/CaltechAUTHORS:ROBpnas25

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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.


Item Type:Article
Additional Information:© 1925 by the National Academy of Sciences. Communicated August 19, 1925. [H.P.R. was a] National Research Fellow in Mathematics.
Record Number:CaltechAUTHORS:ROBpnas25
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:ROBpnas25
Alternative URL:http://www.pnas.org/cgi/reprint/11/10/590
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8577
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:21 Aug 2007
Last Modified:26 Dec 2012 09:40

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