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Ruled Varieties An Introduction to Algebraic Differential Geometry

Ruled varieties are unions of a family of linear spaces. They are objects of algebraic geometry as well as differential geometry, especially if the ruling is developable. This book is an introduction to both aspects, the algebraic and differential one. Starting from very elementary facts, the necess...

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Bibliographic Details
Main Authors: Fischer, Gerd, Piontkowski, Jens (Author)
Format: eBook
Language:English
Published: Wiesbaden Vieweg+Teubner Verlag 2001, 2001
Edition:1st ed. 2001
Series:Advanced Lectures in Mathematics
Subjects:
Algebraic Geometry
Probability Theory
Geometry
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 0 Review from Classical Differential and Projective Geometry
  • 0.1 Developable Rulings
  • 0.2 Vanishing Gauß Curvature
  • 0.3 Hessian Matrices
  • 0.4 Classification of Developable Surfaces in ?3
  • 0.5 Developable Surfaces in ?3(?)
  • 1 Grassmannians
  • 1.1 Preliminaries
  • 1.2 Plücker Coordinates
  • 1.3 Incidences and Duality
  • 1.4 Tangents to Grassmannians
  • 1.5 Curves in Grassmannians
  • 2 Ruled Varieties
  • 2.1 Incidence Varieties and Duality
  • 2.2 Developable Varieties
  • 2.3 The Gauß Map
  • 2.4 The Second Fundamental Form
  • 2.5 Gauß Defect and Dual Defect
  • 3 Tangent and Secant Varieties
  • 3.1 Zak’s Theorems
  • 3.2 Third and Higher Fundamental Forms
  • 3.3 Tangent Varieties
  • 3.4 The Dimension of the Secant Variety
  • List of Symbols

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