Results 201 to 210 of about 1,718 (258)
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1994
Abstract In the previous chapter we laid the foundation for the following formal definition: An affine geometry š(F) of n dimensions over a field Fis a G-space (Ī©, G) equivalent to (Fn, AGL(n, F)).
Peter M Neumann +2 more
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Abstract In the previous chapter we laid the foundation for the following formal definition: An affine geometry š(F) of n dimensions over a field Fis a G-space (Ī©, G) equivalent to (Fn, AGL(n, F)).
Peter M Neumann +2 more
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Affine Transformations in Affine Differential Geometry
Results in Mathematics, 1989For a \(C^{\infty}\) hypersurface immersion f: \(M^ n\to R^{n+1}\), with M orientable, let \(\nabla\) be the affine connection induced by the affine normal and let h be the corresponding (first affine) fundamental form. The author studies the Lie subgroup of those affine transformations of M, with respect to \(\nabla\), that preserve h, namely \(G ...
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On the Minkowski Problem in Affine Geometry
Results in Mathematics, 1991Using the solution of the \(n\)-dimensional Minkowski problem due to \textit{S.-Y. Cheng} and \textit{S. T. Yau} [Commun. Pure Appl. Math. 29, 495-516 (1976; Zbl 0363.53030)], the author obtains an analog of this result in equiaffine differential geometry.
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An Affine Representation for Transversal Geometries
Studies in Applied Mathematics, 1975Pregeometries (matroids) whose independent sets are the partial matchings of a relation (transversal pregeometries) can be canonically imbedded in a freeāsimplicial pregeometry (one whose points lie freely on flats spanned by a simplex). Conversely, all subgeometries of such freeāsimplicial pregeometries are transversal.
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On the Fundamental Theorem of Affine Geometry
Canadian Mathematical Bulletin, 1962The fundamental theorem of affine geometry is an easy corollary of the corresponding projective theorem 2.26 in Artin's Geometric Algebra. However, a simple direct proof based on Lipman's paper [this Bulletin, 4, 265ā278] and his axioms 1 and 2 may be of some interest.Lipman's ...
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