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Isoclinic $n$Planes in Euclidean $2n$Space, Clifford Parallels in Elliptic $(2n1)$Space, and the Hurwitz Matrix Equations
eBook ISBN:  9780821899854 
Product Code:  MEMO/1/41.E 
List Price:  $19.00 
MAA Member Price:  $17.10 
AMS Member Price:  $15.20 
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Isoclinic $n$Planes in Euclidean $2n$Space, Clifford Parallels in Elliptic $(2n1)$Space, and the Hurwitz Matrix Equations
eBook ISBN:  9780821899854 
Product Code:  MEMO/1/41.E 
List Price:  $19.00 
MAA Member Price:  $17.10 
AMS Member Price:  $15.20 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 1; 1961; 112 ppMSC: Primary 51

Table of Contents

Chapters

Introduction

Part I. Isoclinic $n$planes in $E^{2n}$ and Clifford parallel $(n1)$planes in $EL^{2n1}$

1. The $n$planes in $E^{2n}$

2. Condition for two $n$planes in $E^{2n}$ to be isoclinic with each other

3. Maximal sets of mutually isoclinic $n$planes in $E^2n$ and of mutually Cliffordparallel ($n1$)planes in $EL^{2n1}$. Existence of such maximal sets

4. An application: $n$dimensional $C^2$surfaces in $E^{2n}$ with mutually isoclinic tangent $n$planes

5. Some properties of maximal sets

6. Numbers of noncongruent maximal sets — proof of Theorem 3.4

7. Further properties of maximal sets

8. Maximal sets of mutually isoclinic $n$planes in $E^{2n}$ as submanifolds of the Grassmann manifold $G(n,n)$ of $n$planes in $E^{2n}$

Part II. The Hurwitz matrix equations

1. Historial remarks

2. Some lemmas on matrices

3. Reduction of real solutions to quasisolutions

4. Existence of real solutions — the HurwitzRadon theorem

5. Construction and properties of the real solutions

6. Further properties of the real solutions

7. The maximal real solutions

8. The cases $n = 2$, $4$, $8$


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Chapters

Introduction

Part I. Isoclinic $n$planes in $E^{2n}$ and Clifford parallel $(n1)$planes in $EL^{2n1}$

1. The $n$planes in $E^{2n}$

2. Condition for two $n$planes in $E^{2n}$ to be isoclinic with each other

3. Maximal sets of mutually isoclinic $n$planes in $E^2n$ and of mutually Cliffordparallel ($n1$)planes in $EL^{2n1}$. Existence of such maximal sets

4. An application: $n$dimensional $C^2$surfaces in $E^{2n}$ with mutually isoclinic tangent $n$planes

5. Some properties of maximal sets

6. Numbers of noncongruent maximal sets — proof of Theorem 3.4

7. Further properties of maximal sets

8. Maximal sets of mutually isoclinic $n$planes in $E^{2n}$ as submanifolds of the Grassmann manifold $G(n,n)$ of $n$planes in $E^{2n}$

Part II. The Hurwitz matrix equations

1. Historial remarks

2. Some lemmas on matrices

3. Reduction of real solutions to quasisolutions

4. Existence of real solutions — the HurwitzRadon theorem

5. Construction and properties of the real solutions

6. Further properties of the real solutions

7. The maximal real solutions

8. The cases $n = 2$, $4$, $8$
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