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''projective''
3 KB (445 words) - 17:45, 4 June 2020
''in projective geometry''
...the projective plane that leaves fixed all the points of a given straight line (the homology axis) and maps onto themselves all the lines through exactly
2 KB (241 words) - 17:22, 7 February 2011
...uch that shortest paths with respect to this metric are parts of or entire projective straight lines. It is assumed that $R$ does not belong to a hypersurface an
...y discarding some segment (which may reduce to a point) (a metric straight line).
3 KB (497 words) - 16:16, 1 May 2014
...t into correspondence with the point $M_1$ of intersection of the straight line $SM$ with $\pi_1$ (if $SM$ is not parallel to $\pi_1$, see Fig.).
...nerally, let $V$ and $V_1$ be proper subspaces of identical dimension in a projective space $\Omega$ and let $T$ be a subspace of maximal dimension not having po
2 KB (359 words) - 22:17, 11 April 2014
...10_3$-configuration), located in some two-dimensional or three-dimensional projective space.
...ry]]), but it is valid for any projective plane which may be imbedded in a projective space of larger dimension. The spatial case of the Desargues assumption fol
3 KB (435 words) - 11:36, 26 March 2023
$#C+1 = 33 : ~/encyclopedia/old_files/data/P075/P.0705370 Projective straight line,
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5 KB (814 words) - 08:08, 6 June 2020
$#C+1 = 33 : ~/encyclopedia/old_files/data/P075/P.0705380 Projective transformation
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3 KB (417 words) - 08:08, 6 June 2020
...r-quadrics, which are in contact at a point $x$ with a hypersurface $S$ in projective space $P_{n+1}$, is an extension of the Darboux pencil. A (non-developable)
<TR><TD valign="top">[1]</TD> <TD valign="top"> S.P. Finikov, "Projective-differential geometry" , Moscow-Leningrad (1937) (In Russian)</TD></TR><T
2 KB (240 words) - 08:52, 8 April 2023
$#C+1 = 9 : ~/encyclopedia/old_files/data/S090/S.0900400 Straight line
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2 KB (335 words) - 08:23, 6 June 2020
...line). In most cases of interest, $|J|=1$ and so there is only one type of line. The result is called the shadow space over $J$.
...a $(k+1)$-dimensional subspace $Y$ containing $X$, in such a way that the line corresponding to $(X,Y)$ is the set of all $k$-dimensional linear subspaces
3 KB (571 words) - 18:31, 4 August 2014
$#C+1 = 25 : ~/encyclopedia/old_files/data/P075/P.0705300 Projective object of a category
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4 KB (597 words) - 08:08, 6 June 2020
...ology, type if the group acts transitively on the non-fixed points on each line $L$ of the spread which intersects the Baer subplane and fixes one, respect
...ign="top"> V. Jha, N.L. Johnson, "Structure theory for point-Baer and line-Baer collineation groups in affine planes" , ''Proc. Amer. Math. Soc. Conf.
2 KB (305 words) - 17:24, 2 September 2017
...properties are said to be projective; the property of points to be on one line (collinearity), the order of algebraic curves, etc., are such properties.
...ints and lines belong to the improper plane. By completing affine space to projective space, projection becomes one-to-one. A similar procedure applies to an $n$
7 KB (1,119 words) - 13:21, 12 December 2013
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on which the construction of [[Projective differential geometry|projective differential geometry]] is based. They were introduced by G. Fubini (see [[
3 KB (382 words) - 02:34, 14 September 2022
$#C+1 = 122 : ~/encyclopedia/old_files/data/P075/P.0705190 Projective coordinates
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7 KB (1,135 words) - 05:45, 19 March 2022
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dimensional projective space if $ n > 1 $,
3 KB (482 words) - 08:29, 6 June 2020
$#C+1 = 25 : ~/encyclopedia/old_files/data/P075/P.0705170 Projective algebraic set
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3 KB (364 words) - 08:09, 13 July 2022
$#C+1 = 35 : ~/encyclopedia/old_files/data/P075/P.0705210 Projective deformation
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3 KB (529 words) - 08:08, 6 June 2020
...er; but even in the fourth-order neighbourhood there is no unique straight line that could be taken as the third axis of a tetrahedron. In this way one obt
.../TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top"> S.P. Finikov, "Projective differential geometry" , Moscow-Leningrad (1937) (In Russian)</TD></TR></
2 KB (374 words) - 09:17, 19 November 2018
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An involutory correlation of an $ n $-dimensional projective space with an anti-symmetric operator. Suppose that the null system has the
4 KB (553 words) - 02:25, 16 June 2022