Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T08:03:42.582Z Has data issue: false hasContentIssue false

The biaxial surfaces, and the equivalence of binary forms

Published online by Cambridge University Press:  24 October 2008

B. Segre
Affiliation:
The UniversityManchester

Extract

The problem of the equivalence of binary forms is of great importance, both historically and intrinsically, and is also significant for the problems of the so-called canonical and automorphic forms. It consists in deciding whether two given forms are equivalent, i.e. transformable one into the other linearly, and, when they are, in finding all the linear substitutions transforming one form into the other.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1945

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Beltrami, E. Sur la courbure de quelques lignes tracées sur une surface. Nouv. Ann. Math. (2) 4 (1865), 258–67 (or Opere Matematiche, 1, 255–61).Google Scholar
(2)Beltrami, E. Dimostrazione di due formule del sig. Bonnet. Giorn. Mat. 4 (1866), 123–7 (or Opere Matematiche, 2, 297–301).Google Scholar
(3)Burnside, W. S. and Panton, A. W. Theory of equations, 2, 4th ed. (Dublin, 1901).Google Scholar
(4)Cesàro, E. Elementares Lehrbuch der algebraischen Analysis und der Infinitesimalrechnung (Leipzig, 1904).Google Scholar
(5)Darboux, G. Leçons sur la théorie générale des surfaces, 1 (Paris, 1887).Google Scholar
(6)Elliott, E. B. An introduction to the algebra of quantics (Oxford, 1895).Google Scholar
(7)Enneper, A. Ueber asymptotische Linien. Nachr. Ges. Wiss. Göttingen (1870), pp. 493510.Google Scholar
(8)Grace, J. H. and Young, A. The algebra of invariants (Cambridge, 1903).Google Scholar
(9)Jamet, V. Sur les surfaces et les courbes tétraédrales symétriques. Ann. Ec. Norm. Sup. (III), 4 (1887), Supplément, pp. 378.CrossRefGoogle Scholar
(10)Koenigs, G. Sur les propriétés infinitésimales de l'espace réglé (Thèse, Paris, 1882).Google Scholar
(11)Lie, S. Ueber die Reciprocitäts-Verhältnisse des Reye'schen Complexes. Nachr. Ges. Wiss. Göttingen (1870), pp. 5366.Google Scholar
(12)Picard, É. Traité d'analyse, 1 (Paris, 1891), and 2 (Paris, 1893).Google Scholar
(13)Salmon, G. Analytic geometry of three dimensions, 2, 5th ed. (London, 1915).Google Scholar
(14)Salmon, G. Lessons introductory to the modern higher algebra, 3rd ed. (Dublin, 1876).Google Scholar
(15)Segre, B. The non-singular cubic surfaces (Oxford, 1942).Google Scholar
(16)Segre, B. The maximum number of lines lying on a quartic surface. Quart. J. Math. 14 (1943), 8696.CrossRefGoogle Scholar
(17)Segre, B. On the quartic surface Proc. Cambridge Phil. Soc. 40 (1944), 121–45.CrossRefGoogle Scholar
(18)Segre, B. Equivalenza ed automorfismi delle forme binarie in un dato anello o campo numerico.—Due to appear in the Revista Univ. Nac. Tucuman.Google Scholar
(19)Segre, B. On tac-invariants of two curves in a projective space.—Due to appear in the Quart. J. Math.Google Scholar
(20)Segre, B. On arithmetical properties of quadric and quartic surfaces.—Due to appear in the J. London Math. Soc.Google Scholar
(21)Segre, C. Su alcuni punti singolari delle curve algebriche e sulla linea parabolica di una superficie. R.C. Accad. Lincei (v), 6 (1897)2, 168–75.Google Scholar
(22)Segre, C. Sulla generazione delle superficie che ammettono un doppio sistema coniugato di coni circoscritti. Atti Accad. Torino, 43 (1908), 985–97.Google Scholar
(23)Segre, C. Sugli elementi curvilinei, che hanno comune la tangente e il piano osculatore. R.C. Accad. Lincei (v), 33 (1924)1, 325–9.Google Scholar