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Representation of the planes of five-dimensional space

Published online by Cambridge University Press:  24 October 2008

C. V. Hanumanta Rao
C. V. Hanumanta Rao
Affiliation:
Trinity College
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Extract

The planes of a given S5 can be represented by the points of a locus V9 in space of nineteen dimensions. This locus is a double locus on a certain other manifold V14, and the tangent spaces of the V9 generate a W18. Segre has a memoir on the subject of these loci, in which he arrives at his results by a series of short steps, the argument being mainly geometrical.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 26 , Issue 1 , January 1930 , pp. 72 - 81
Copyright
Copyright © Cambridge Philosophical Society 1930

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References

* Annali di mat. 27 (1918), 75–123.CrossRefGoogle Scholar

† Encykl. Math. Wiss, III C 7, Mehrdimensionale Räume, p. 792.

* Cf. Severi, , Annali di mat. 24 (1915), 89–120, where a similar representation is worked out; the present one is more symmetrical. The symbol 010 stands for a sequence of ten zeros.CrossRefGoogle Scholar

† The x 2, x 3 may really be taken as zero, and the x 4 as unity, leaving thus only a double infinity.

* Rendiconti Palermo, 5 (1891), 192–204.Google Scholar

† This is substantially what is stated in the article of Severi cited above.