Zeitschriftenartikel: „Geometry, Projective“

1

Machale, Des, and H. S. M. Coxeter. "Projective Geometry." Mathematical Gazette 74, no. 467 (March 1990): 82. http://dx.doi.org/10.2307/3618883.

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2

Rota, Gian-Carlo. "Projective geometry." Advances in Mathematics 77, no. 2 (October 1989): 263. http://dx.doi.org/10.1016/0001-8708(89)90023-6.

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3

Tabatabaeifar, Tayebeh, Behzad Najafi, and Akbar Tayebi. "Weighted projective Ricci curvature in Finsler geometry." Mathematica Slovaca 71, no. 1 (January 29, 2021): 183–98. http://dx.doi.org/10.1515/ms-2017-0446.

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Abstract In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

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4

Ubaidillah, Muhammad Izzat. "Proyeksi Geometri Fuzzy pada Ruang." CAUCHY 2, no. 3 (November 15, 2012): 139. http://dx.doi.org/10.18860/ca.v2i3.3123.

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<div class="standard"><a id="magicparlabel-481">Fuzzy geometry is an outgrowth of crisp geometry, which in crisp geometry elements are exist and not exist, but also while on fuzzy geometry elements are developed by thickness which is owned by each of these elements. Crisp projective geometries is the formation of a shadow of geometries element projected on the projectors element, with perpendicular properties which are represented by their respective elemental, the discussion focused on the results of the projection coordinates. While the fuzzy projective geometries have richer discussion, which includes about coordinates of projection results, the mutual relation of each element and the thickness of each element. This research was conducted to describe and analyzing procedure fuzzy projective geometries on the plane and explain the differences between crisp projective geometries and fuzzy projective geometries on plane.</a></div>

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Calderbank, David, Michael Eastwood, Vladimir Matveev, and Katharina Neusser. "C-projective geometry." Memoirs of the American Mathematical Society 267, no. 1299 (September 2020): 0. http://dx.doi.org/10.1090/memo/1299.

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6

Kanatani, Kenichi. "Computational projective geometry." CVGIP: Image Understanding 54, no. 3 (November 1991): 333–48. http://dx.doi.org/10.1016/1049-9660(91)90034-m.

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7

Erdnüß, B. "MEASURING IN IMAGES WITH PROJECTIVE GEOMETRY." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-1 (September 26, 2018): 141–48. http://dx.doi.org/10.5194/isprs-archives-xlii-1-141-2018.

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<p><strong>Abstract.</strong> There is a fundamental relationship between projective geometry and the perspective imaging geometry of a pinhole camera. Projective scales have been used to measure within images from the beginnings of photogrammetry, mostly the cross-ratio on a straight line. However, there are also projective frames in the plane with interesting connections to affine and projective geometry in three dimensional space that can be utilized for photogrammetry. This article introduces an invariant on the projective plane, describes its relation to affine geometry, and how to use it to reduce the complexity of projective transformations. It describes how the invariant can be use to measure on projectively distorted planes in images and shows applications to this in 3D reconstruction. The article follows two central ideas. One is to measure coordinates in an image relatively to each other to gain as much invariance of the viewport as possible. The other is to use the remaining variance to determine the 3D structure of the scene and to locate the camera centers. For this, the images are projected onto a common plane in the scene. 3D structure not on the plane occludes different parts of the plane in the images. From this, the position of the cameras and the 3D structure are obtained.</p>

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8

Chaput, Pierre-Emmanuel. "Geometry over composition algebras: Projective geometry." Journal of Algebra 298, no. 2 (April 2006): 340–62. http://dx.doi.org/10.1016/j.jalgebra.2006.02.008.

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9

Song, Xiao Zhuang, Ming Liang Lu, and Tao Qin. "Projective Geometry on the Structure of Geometric Composition Analysis Application." Applied Mechanics and Materials 166-169 (May 2012): 127–30. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.127.

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The analysis rule of geometry composition analysis in building structure must rely on geometry theory, while the traditional Euclidean geometry theory can not solve some building structures problems of the geometry components. This problem can be solved in the use of projective geometry theory. In this paper we introduce the proof of projective geometry in the geometry composition analysis and we discuss the application of this theory.

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10

Gupta, K. C., and Suryansu Ray. "Fuzzy plane projective geometry." Fuzzy Sets and Systems 54, no. 2 (March 1993): 191–206. http://dx.doi.org/10.1016/0165-0114(93)90276-n.

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11

Dillon, Meighan. "Projective Geometry for All." College Mathematics Journal 45, no. 3 (May 2014): 169–78. http://dx.doi.org/10.4169/college.math.j.45.3.169.

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12

López Peña, Javier, and Oliver Lorscheid. "Projective geometry for blueprints." Comptes Rendus Mathematique 350, no. 9-10 (May 2012): 455–58. http://dx.doi.org/10.1016/j.crma.2012.05.001.

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13

E. Arif, Ghassan. "Intuitionistic fuzzy projective geometry." Journal of University of Anbar for Pure Science 3, no. 1 (April 1, 2009): 143–47. http://dx.doi.org/10.37652/juaps.2009.15413.

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14

Sauer, Tilman, and Tobias Schütz. "Einstein on involutions in projective geometry." Archive for History of Exact Sciences 75, no. 5 (January 8, 2021): 523–55. http://dx.doi.org/10.1007/s00407-020-00270-z.

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AbstractWe discuss Einstein’s knowledge of projective geometry. We show that two pages of Einstein’s Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his Princeton years. By this correspondence, we show that the sketches are all related to a common theme, the discussion of involution in a projective geometry setting with particular emphasis on the infinite point. We offer a conjecture as to the probable purpose of these geometric considerations.

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15

Uchino, K. "Arnold's Projective Plane and -Matrices." Advances in Mathematical Physics 2010 (2010): 1–9. http://dx.doi.org/10.1155/2010/956128.

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We will explain Arnold's 2-dimensional (shortly, 2D) projective geometry (Arnold, 2005) by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular -matrices is the pencil of tangent lines of a quadratic curve on Arnold's projective plane.

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16

Lashkhi, A. A. "General geometric lattices and projective geometry of modules." Journal of Mathematical Sciences 74, no. 3 (April 1995): 1044–77. http://dx.doi.org/10.1007/bf02362832.

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17

Gunn, Charles G. "Doing Euclidean Plane Geometry Using Projective Geometric Algebra." Advances in Applied Clifford Algebras 27, no. 2 (October 18, 2016): 1203–32. http://dx.doi.org/10.1007/s00006-016-0731-5.

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18

Yur'ev, D. V. "Complex projective geometry and quantum projective field theory." Theoretical and Mathematical Physics 101, no. 3 (December 1994): 1387–403. http://dx.doi.org/10.1007/bf01035459.

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19

Ito, Atsushi, Makoto Miura, and Kazushi Ueda. "Projective Reconstruction in Algebraic Vision." Canadian Mathematical Bulletin 63, no. 3 (November 13, 2019): 592–609. http://dx.doi.org/10.4153/s0008439519000687.

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AbstractWe discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the projective reconstruction theorem by Hartley and Schaffalitzky.

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20

WAN, C., and J. SATO. "Multiple View Geometry under Projective Projection in Space-Time." IEICE Transactions on Information and Systems E91-D, no. 9 (September 1, 2008): 2353–59. http://dx.doi.org/10.1093/ietisy/e91-d.9.2353.

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21

Rubin, Jacques. "Applications of a Particular Four-Dimensional Projective Geometry to Galactic Dynamics." Galaxies 6, no. 3 (August 3, 2018): 83. http://dx.doi.org/10.3390/galaxies6030083.

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Relativistic localizing systems that extend relativistic positioning systems show that pseudo-Riemannian space-time geometry is somehow encompassed in a particular four-dimensional projective geometry. The resulting geometric structure is then that of a generalized Cartan space (also called Cartan connection space) with projective connection. The result is that locally non-linear actions of projective groups via homographies systematically induce the existence of a particular space-time foliation independent of any space-time dynamics or solutions of Einstein’s equations for example. In this article, we present the consequences of these projective group actions and this foliation. In particular, it is shown that the particular geometric structure due to this foliation is similar from a certain point of view to that of a black hole but not necessarily based on the existence of singularities. We also present a modified Newton’s laws invariant with respect to the homographic transformations induced by this projective geometry. Consequences on galactic dynamics are discussed and fits of galactic rotational velocity curves based on these modifications which are independent of any Modified Newtonian Dynamics (MOND) or dark matter theories are presented.

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22

Kalmbach H.E., Gudrun. "Projective Gravity." International Journal of Contemporary Research and Review 9, no. 03 (March 13, 2018): 20181–83. http://dx.doi.org/10.15520/ijcrr/2018/9/03/466.

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In [1] and [3] it was pointed out that octonians can replace an infinite dimensional Hilbert space and psi-waves descriptions concerning the states of deuteron which are finite in number. It is then clear that gravity needs projective and projection geometry to be described in a unified way with the three other basic forces of physics.

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23

Burn, Bob, Lars Kadison, and Matthias T. Kromann. "Projective Geometry and Modern Algebra." Mathematical Gazette 80, no. 488 (July 1996): 446. http://dx.doi.org/10.2307/3619609.

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24

Delphenich, D. H. "Projective geometry and special relativity." Annalen der Physik 518, no. 3 (February 22, 2006): 216–46. http://dx.doi.org/10.1002/andp.20065180304.

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25

Grigorenko, A. N. "Geometry of projective Hilbert space." Physical Review A 46, no. 11 (December 1, 1992): 7292–94. http://dx.doi.org/10.1103/physreva.46.7292.

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26

Givental, A. B. "Homological geometry I. Projective hypersurfaces." Selecta Mathematica 1, no. 2 (September 1995): 325–45. http://dx.doi.org/10.1007/bf01671568.

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27

Frescura, F. A. M. "Projective spinor geometry and prespace." Foundations of Physics 18, no. 8 (August 1988): 777–808. http://dx.doi.org/10.1007/bf01889310.

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28

Čap, A., A. R. Gover, and H. R. Macbeth. "Einstein metrics in projective geometry." Geometriae Dedicata 168, no. 1 (February 3, 2013): 235–44. http://dx.doi.org/10.1007/s10711-013-9828-3.

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29

Schwartz, Richard Evan, and Serge Tabachnikov. "Elementary Surprises in Projective Geometry." Mathematical Intelligencer 32, no. 3 (April 24, 2010): 31–34. http://dx.doi.org/10.1007/s00283-010-9137-8.

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30

Aicardi, Francesca. "Projective geometry from Poisson algebras." Journal of Geometry and Physics 61, no. 8 (August 2011): 1574–86. http://dx.doi.org/10.1016/j.geomphys.2011.03.010.

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31

Kohn, Kathlén, and Kristian Ranestad. "Projective Geometry of Wachspress Coordinates." Foundations of Computational Mathematics 20, no. 5 (November 11, 2019): 1135–73. http://dx.doi.org/10.1007/s10208-019-09441-z.

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Abstract We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane arrangement. This generalizes the construction of the adjoint curve of a polygon by Wachspress (A rational finite element basis, Academic Press, New York, 1975). The defining polynomial of our adjoint hypersurface is the adjoint polynomial introduced by Warren (Adv Comput Math 6:97–108, 1996). This is a key ingredient for the definition of Wachspress coordinates, which are barycentric coordinates on an arbitrary convex polytope. The adjoint polynomial also appears both in algebraic statistics, when studying the moments of uniform probability distributions on polytopes, and in intersection theory, when computing Segre classes of monomial schemes. We describe the Wachspress map, the rational map defined by the Wachspress coordinates, and the Wachspress variety, the image of this map. The inverse of the Wachspress map is the projection from the linear span of the image of the adjoint hypersurface. To relate adjoints of polytopes to classical adjoints of divisors in algebraic geometry, we study irreducible hypersurfaces that have the same degree and multiplicity along the non-faces of a polytope as its defining hyperplane arrangement. We list all finitely many combinatorial types of polytopes in dimensions two and three for which such irreducible hypersurfaces exist. In the case of polygons, the general such curves are elliptic. In the three-dimensional case, the general such surfaces are either K3 or elliptic.

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32

Trappey, Amy J. C., and Shankaran Matrubhutam. "Fixture configuration using projective geometry." Journal of Manufacturing Systems 12, no. 6 (January 1993): 486–95. http://dx.doi.org/10.1016/0278-6125(93)90345-t.

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33

Safari, R., N. Narasimhamurthi, M. Shridhar, and M. Ahmadi. "Document registration using projective geometry." IEEE Transactions on Image Processing 6, no. 9 (September 1997): 1337–41. http://dx.doi.org/10.1109/83.623198.

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34

Dodson, C. T. J. "Fréchet geometry via projective limits." International Journal of Geometric Methods in Modern Physics 11, no. 07 (August 2014): 1460017. http://dx.doi.org/10.1142/s0219887814600172.

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Fréchet spaces of sections arise naturally as configurations of a physical field. Some recent work in Fréchet geometry is briefly reviewed and some suggestions for future work are offered. An earlier result on the structure of second tangent bundles in the finite-dimensional case was extended to infinite-dimensional Banach manifolds and Fréchet manifolds that could be represented as projective limits of Banach manifolds. This led to further results concerning the characterization of second tangent bundles and differential equations in the more general Fréchet structure needed for applications.

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35

McKay, Benjamin. "Rigid geometry on projective varieties." Mathematische Zeitschrift 272, no. 3-4 (November 12, 2011): 761–91. http://dx.doi.org/10.1007/s00209-011-0957-9.

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36

Delphenich, D. H. "Projective geometry and special relativity." Annalen der Physik 15, no. 3 (March 15, 2006): 216–46. http://dx.doi.org/10.1002/andp.200510179.

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37

Bogomolov, Fedor, and Yuri Tschinkel. "Galois Theory and Projective Geometry." Communications on Pure and Applied Mathematics 66, no. 9 (June 26, 2013): 1335–59. http://dx.doi.org/10.1002/cpa.21466.

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38

Bădescu, Lucian. "Special chapters of projective geometry." Rendiconti del Seminario Matematico e Fisico di Milano 69, no. 1 (December 1999): 239–326. http://dx.doi.org/10.1007/bf02938684.

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39

Hestenes, David, and Renatus Ziegler. "Projective geometry with Clifford algebra." Acta Applicandae Mathematicae 23, no. 1 (April 1991): 25–63. http://dx.doi.org/10.1007/bf00046919.

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40

Gros, P., R. Hartley, R. Mohr, and L. Quan. "How Useful is Projective Geometry?" Computer Vision and Image Understanding 65, no. 3 (March 1997): 442–46. http://dx.doi.org/10.1006/cviu.1996.0496.

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41

ANDRUCHOW, ESTEBAN, GUSTAVO CORACH, and DEMETRIO STOJANOFF. "PROJECTIVE SPACE OF A C*-MODULE." Infinite Dimensional Analysis, Quantum Probability and Related Topics 04, no. 03 (September 2001): 289–307. http://dx.doi.org/10.1142/s0219025701000516.

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Let X be a right Hilbert C*-module over A. We study the geometry and the topology of the projective space [Formula: see text] of X, consisting of the orthocomplemented submodules of X which are generated by a single element. We also study the geometry of the p-sphere Sp(X) and the natural fibration [Formula: see text], where Sp(X) = {x ∈ X: <x, x> = p}, for p ∈ A a projection. The projective space and the p-sphere are shown to be homogeneous differentiable spaces of the unitary group of the algebra ℒA(X) of adjointable operators of X. The homotopy theory of these spaces is examined.

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42

Li, Xinsheng, and Xuedong Yuan. "Fundamental Matrix Computing Based on 3D Metrical Distance." Algorithms 14, no. 3 (March 15, 2021): 89. http://dx.doi.org/10.3390/a14030089.

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To reconstruct point geometry from multiple images, computation of the fundamental matrix is always necessary. With a new optimization criterion, i.e., the re-projective 3D metric geometric distance rather than projective space under RANSAC (Random Sample And Consensus) framework, our method can reveal the quality of the fundamental matrix visually through 3D reconstruction. The geometric distance is the projection error of 3D points to the corresponding image pixel coordinates in metric space. The reasonable visual figures of the reconstructed scenes are shown but only some numerical result were compared, as is standard practice. This criterion can lead to a better 3D reconstruction result especially in 3D metric space. Our experiments validate our new error criterion and the quality of fundamental matrix under the new criterion.

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43

Bidabad, Behroz, and Maryam Sepasi. "On a projectively invariant pseudo-distance in Finsler geometry." International Journal of Geometric Methods in Modern Physics 12, no. 04 (April 2015): 1550043. http://dx.doi.org/10.1142/s0219887815500437.

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Here, a nonlinear analysis method is applied rather than classical one to study projective changes of Finsler metrics. More intuitively, a projectively invariant pseudo-distance is introduced and characterized with respect to the Ricci tensor and its covariant derivatives.

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44

Stebletsova, Vera, and Yde Venema. "Undecidable theories of Lyndon algebras." Journal of Symbolic Logic 66, no. 1 (March 2001): 207–24. http://dx.doi.org/10.2307/2694918.

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AbstractWith each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski's axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class of projective geometries which contains an infinite projective geometry of dimension at least three, then the class L(G) of Lyndon algebras associated with projective geometries in G has an undecidable equational theory. In our proof we develop and use a connection between projective geometries and diagonal-free cylindric algebras.

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45

Pfeiffer, Thorsten, and Stefan E. Schmidt. "Projective mappings between projective lattice geometries." Journal of Geometry 54, no. 1-2 (November 1995): 105–14. http://dx.doi.org/10.1007/bf01222858.

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46

Artstein-Avidan, Shiri, and Boaz A. Slomka. "The fundamental theorems of affine and projective geometry revisited." Communications in Contemporary Mathematics 19, no. 05 (August 18, 2016): 1650059. http://dx.doi.org/10.1142/s0219199716500590.

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The fundamental theorem of affine geometry is a classical and useful result. For finite-dimensional real vector spaces, the theorem roughly states that a bijective self-mapping which maps lines to lines is affine-linear. In this paper, we prove several generalizations of this result and of its classical projective counterpart. We show that under a significant geometric relaxation of the hypotheses, namely that only lines parallel to one of a fixed set of finitely many directions are mapped to lines, an injective mapping of the space must be of a very restricted polynomial form. We also prove that under mild additional conditions the mapping is forced to be affine-additive or affine-linear. For example, we show that five directions in three-dimensional real space suffice to conclude affine-additivity. In the projective setting, we show that [Formula: see text] fixed projective points in real [Formula: see text]-dimensional projective space, through which all projective lines that pass are mapped to projective lines, suffice to conclude projective-linearity.

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WESSLER, MARKUS. "A GEOMETRIC VERSION OF DYSON'S LEMMA FOR FACTORS OF ARBITRARY DIMENSION." International Journal of Mathematics 13, no. 01 (February 2002): 43–65. http://dx.doi.org/10.1142/s0129167x02001149.

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This paper generalizes the geometric part of the Esnault–Viehweg paper on Dyson's Lemma for a product of projective lines. Using the method of weak positivity from algebraic geometry, we are able to study products of smooth projective varieties of arbitrary dimension and to prove a geometric analogue of Dyson's Lemma for this case. Our main result is in fact a quantitative version of Faltings' product theorem.

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48

Chen, Wen-Haw, and Ja’faruddin. "Traditional Houses and Projective Geometry: Building Numbers and Projective Coordinates." Journal of Applied Mathematics 2021 (August 31, 2021): 1–25. http://dx.doi.org/10.1155/2021/9928900.

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The natural mathematical abilities of humans have advanced civilizations. These abilities have been demonstrated in cultural heritage, especially traditional houses, which display evidence of an intuitive mathematics ability. Tribes around the world have built traditional houses with unique styles. The present study involved the collection of data from documentation, observation, and interview. The observations of several traditional buildings in Indonesia were based on camera images, aerial camera images, and documentation techniques. We first analyzed the images of some sample of the traditional houses in Indonesia using projective geometry and simple house theory and then formulated the definitions of building numbers and projective coordinates. The sample of the traditional houses is divided into two categories which are stilt houses and nonstilt house. The present article presents 7 types of simple houses, 21 building numbers, and 9 projective coordinates.

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49

Janic, Milan, and Dejan Tanikic. "Geometry of straight lines pencils." Facta universitatis - series: Architecture and Civil Engineering 2, no. 4 (2002): 291–94. http://dx.doi.org/10.2298/fuace0204291j.

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This paper considers a pencil of straight Unes in the Euclidean plane as well as the same pencil of straight lines in the projective plane where the projective geometry model M" is defined with its points forming the sets of (n-l) collinear points, whose supporting straight lines belong to the considered pencil of straight lines.

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Kruglikov, Boris, Vladimir Matveev, and Dennis The. "Submaximally symmetric c-projective structures." International Journal of Mathematics 27, no. 03 (March 2016): 1650022. http://dx.doi.org/10.1142/s0129167x16500221.

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[Formula: see text]-projective structures are analogues of projective structures in the almost complex setting. The maximal dimension of the Lie algebra of [Formula: see text]-projective symmetries of a complex connection on an almost complex manifold of [Formula: see text]-dimension [Formula: see text] is classically known to be [Formula: see text]. We prove that the submaximal dimension is equal to [Formula: see text]. If the complex connection is minimal (encoded as a normal parabolic geometry), the harmonic curvature of the [Formula: see text]-projective structure has three components and we specify the submaximal symmetry dimensions and the corresponding geometric models for each of these three pure curvature types. If the connection is non-minimal, we introduce a modified normalization condition on the parabolic geometry and use this to resolve the symmetry gap problem. We prove that the submaximal symmetry dimension in the class of Levi-Civita connections for pseudo-Kähler metrics is [Formula: see text], and specializing to the Kähler case, we obtain [Formula: see text]. This resolves the symmetry gap problem for metrizable [Formula: see text]-projective structures.

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Zeitschriftenartikel zum Thema „Geometry, Projective“

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