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Geometry of Aggregates
Geometry of Aggregates

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  • 作 者:
  • 出 版 社:Koninklyke Van Gorcum & Comp.
  • 出版年份:1957
  • ISBN:
  • 页数:100 页
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INTRODUCTION 1

PREPARATION 7

1.The projective r-dimensional space Sr 7

2.The dual space 8

3.Subspaces of Sr;Substars of r 9

4.Algebraic manifolds 11

5.Projections 14

6.Birational correspondences 14

CHAPTER Ⅰ -SEGRE MANIFOLDS 16

1.The twofold projective space 16

2.The manifold[m;n]h 19

3.The prime-manifold]m;n[h 26

4.Correlations 30

CHAPTER Ⅱ -PROJECTIVELY GENERATED MANIFOLDS IN ARBITRARY SPACES 36

1.Projectively generated manifolds in a space of arbitrary dimension 36

2.Submanifolds of Sr 40

3.Pairing Theorems and Double-N Theorem 44

4.Aggregates 48

CHAPTER Ⅲ -BIRATIONAL CORRESPONDENCES 52

1.The birationally related manifolds Sr and Sm 52

2.Representation of Sr and Sm by [m;r]0 SN-n-1 57

3.Apolar systems of aggregates 61

CHAPTER Ⅳ -PENCILS OF TWO-DIMENSIONAL AGGREGAEST IN THREE-SPACE 65

1.The linear system of 1 two-dimensional contravariant aggregates in S3 65

2.The relation between the manifolds S3 and S2 66

3.A representation of S3 in the matrix-space S11 68

4.Representation of S2 in the matrix-space S11 71

5.Particular systems of aggregates ]l|2[0 S3 73

CHAPTER Ⅴ -NETS OF TWO-DIMENSIONAL AGGREGATES IN THREE-SPACE 78

1.The linear system of 2 two-dimensional contravariant aggregates in S3 78

2.The relation between the manifolds S3 and S2 79

3.The representation of S3 in the matrix-space S11 83

4.The representation of S2 in the matrix-space S11 85

5.Particular systems of aggregates ]2|2[0 S3 87

CHAPTER Ⅵ -A SURVEY OF FURTHER DEVELOPMENTS 93

1.The system of aggregates ]3|2[0 S3 93

2.The system of aggregates ]4|2[0 S3 94

REFERENCES 96

INDEX 98

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