A QUADRATIC TRANSFORMATION OF THETHREE-DIMENSIONAL SPACE OF ALL CONICSTHROUGH TWO POINTS OF A PROJECTIVE PLANE

Giorgio Donati

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A QUADRATIC TRANSFORMATION OF THETHREE-DIMENSIONAL SPACE OF ALL CONICSTHROUGH TWO POINTS OF A PROJECTIVE PLANE

机译：投影平面上两点所有圆锥的三维空间的二次变换

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摘要

Using the Steiner's method of projective generation of conics and its dualwe define two projective mappings of a double contact pencil of conics into itself andwe prove that one is the inverse of the other. We show that these projective mappingsare induced by quadratic transformations of the three-dimensional projective space of allconics through two distinct points of a projective plane.

机译：使用Steiner的圆锥形射影生成方法及其对偶关系，我们定义了圆锥形双接触铅笔本身的两个射影映射，并证明了一个是另一个的倒数。我们表明，这些投影映射是通过投影平面的两个不同点，通过二次曲面的三维圆锥投影空间的二次变换而诱发的。

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来源
《Demonstratio Mathematica》 |2009年第3期|共7页
作者
Giorgio Donati;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
pencils of conics; projectivities;

机译：圆锥形铅笔;投射性;

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专利

1. A QUADRATIC TRANSFORMATION OF THETHREE-DIMENSIONAL SPACE OF ALL CONICSTHROUGH TWO POINTS OF A PROJECTIVE PLANE [J] . Giorgio Donati Demonstratio Mathematica . 2009,第3期

机译：投影平面上两点所有圆锥的三维空间的二次变换
2. On special quadratic birational transformations of a projective space into a hypersurface [J] . Giovanni Staglianò Rendiconti del Circolo Matematico di Palermo . 2012,第3期

机译：关于投影空间到超曲面的特殊二次Birational变换
3. On special quadratic birational transformations of a projective space into a hypersurface [J] . Staglianò G. Rendiconti del Circolo Matematico di Palermo . 2012,第3期

机译：关于投影空间到超曲面的特殊二次Birational变换
4. Single plane model extension using projective transformations and data fusion [C] . Collins, R.T. . 1992

机译：使用投影变换和数据融合的单平面模型扩展
5. Subspace projection methods for the quadratic eigenvalue problems. [D] . Hoffnung, Leonard. 2004

机译：二次特征值问题的子空间投影方法。
6. Eigenspace-based beamformer using oblique signal subspace projection for ultrasound plane-wave imaging [O] . Saeid Aliabadi, Yuanyuan Wang, Jinhua Yu, 2016

机译：基于本征空间的波束形成器使用倾斜信号子空间投影进行超声平面波成像
7. On special quadratic birational transformations of a projective space into a hypersurface [O] . Staglianò, Giovanni 2012

机译：关于投射空间的特殊二次双向变换进入超曲面

A QUADRATIC TRANSFORMATION OF THETHREE-DIMENSIONAL SPACE OF ALL CONICSTHROUGH TWO POINTS OF A PROJECTIVE PLANE

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