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Projective Differential Geometry of Systems of Linear Partial Differential Equations

  • Beniamino Segre
Conference paper
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 13)

Abstract

—In S n over a field F which will generally be either the real or the complex one — consider a surface Φ defined as the locus of points x whose projective coordinates (x(0) x(1),..., x(n)) are functions of two parameters u and v. These functions will all be supposed continuous with derivatives of sufficiently high order.x u will denote the point\(\left( {\frac{{\partial {x^{\left( 0 \right)}}}}{{\partial u}},\frac{{\partial {x^{\left( 1 \right)}}}}{{\partial u}},...,\frac{{\partial {x^{\left( n \right)}}}}{{\partial u}}} \right) \) and other derivatives of x will be similarly denoted; x u and x v are called the first derived points of x. The tangent plane at x to Φ is the plane joining the independent points x, x u , x v .

Keywords

LAPLACE Equation Tangent Plane Linear Partial Differential Equation Topological Variety VERONESE Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Beniamino Segre
    • 1
  1. 1.Istituto MatematicoUniversità di RomaRomaItaly

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