A quadratic transformation of the three-dimensional space of all conics throught two points of a projective plane

• Autorzy: Donati G.
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Steiner method; conics

PL

metoda Steinera; krzywe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 3
• Strony: 619--625
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Donati G.

• Dipartimento di Matematica e Applicazioni Universita di Napoli "Federico II" Via Claudio 21 80125 Napoli, Italy,

Bibliografia

• [1] L. Campedelli, Lezioni di Geometria, Second Edition, CEDAM, Padova, 1953.
• [2] H. S. M. Coxeter, Projective Geometry, Second Edition, University of Toronto Press, Toronto, 1974.
• [3] J. G. Semple, G. T. Kneebone, Algebraic Projective Geometry, Oxford at the Clarendon Press, Oxford, 1952.
• [4] F. Severi, Geometria Proiettiva, Vallecchi, Firenze, 1926.
• [5] J. Steiner, Systematische Entwicklung der Abhängigkeit geometrischer Gestalten von einander, Reimer, Berlin, 1832.