Selected topics in three dimensional synthetic projective geometry

Preface......Page 1
Preliminaries......Page 5
1: Projectivitie between primitive forms of one and two dimensions......Page 10
2: Projectivities in three-dimensional space.......Page 24
3: Introduction to curves and surfaces in three-dimensional projective space.......Page 40
4: Surfaces of the second degree in three-dimensional projective space.......Page 49
5: Involutory collineations and polarities in three-dimensional projective space.......Page 69
6: Foundations of three-dimensional Euclidean and non-Euclidean geometry.......Page 86
7: Fundamental notions of line geometry in three-dimensional projective space.......Page 101
8: Linear complexes of lines in three-dimensional projective space.......Page 112
9: Linear congruences of lines in three-dimensional projective space.......Page 127
10: Families of lines in three-dimensional projective space generated by collineations between bundles and fields.......Page 143
11: Twisted cubics and cubic developables in three-dimensional projective space.......Page 167
12: Collineations in three-dimensional projective space: Tetrahedral Quadratic Complexes.......Page 184
13 Part I: Non-Euclidean, affine and Euclidean properties of linear families of lines in three-dimensional projective space......Page 196
13 Part II: Non-Euclidean, affine and Euclidean properties of linear families of lines in three-dimensional projective space......Page 207
14: Reciprocal linear complexes in three-dimensional projective space.......Page 226
15: Linear manifolds of linear complexes in three-dimensional projective space.......Page 235
16: Two-dimensional manifolds of linear complexes and their induced polarities in three-dimensional projective space.......Page 250
17: The five-dimensional linear manifold of linear complexes.......Page 259
18: Fundamental Complexes.......Page 267
References......Page 277
Index......Page 280