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- W2080661708 abstract "Introduction. In a previous paper(1), the author has established a theory of the projective differential geometry of conjugate nets in a linear space S4 of four dimensions. The purpose of the present paper is to extend the theory to a general linear space Sn (n _4). In ?1 a completely integrable system of linear homogeneous partial differential equations, together with its integrability conditions, is introduced by a purely geometric method defining a conjugate net N., in the space Sn except for a projective transformation. A canonical form of the system of differential equations is obtained in ?2 by a geometric determination. In ?3 we deduce the conditions of immovability for a point and a hyperplane in the space Sn, relative to an invariant local pyramid of reference associated with a point x of the conjugate net Nl. ??4, 5, 6 are devoted to proving the following theorems respectively." @default.
- W2080661708 created "2016-06-24" @default.
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- W2080661708 date "1951-02-01" @default.
- W2080661708 modified "2023-09-24" @default.
- W2080661708 title "A general theory of conjugate nets in projective hyperspace" @default.
- W2080661708 doi "https://doi.org/10.1090/s0002-9947-1951-0043515-4" @default.
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