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Isoclinic $n$-Planes in Euclidean $2n$-Space, Clifford Parallels in Elliptic $(2n-1)$-Space, and the Hurwitz Matrix Equations
| eBook ISBN: | 978-0-8218-9985-4 |
| 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 $(2n-1)$-Space, and the Hurwitz Matrix Equations
| eBook ISBN: | 978-0-8218-9985-4 |
| Product Code: | MEMO/1/41.E |
| List Price: | $19.00 |
| MAA Member Price: | $17.10 |
| AMS Member Price: | $15.20 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 1; 1961; 112 ppMSC: Primary 51
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Table of Contents
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Chapters
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Introduction
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Part I. Isoclinic $n$-planes in $E^{2n}$ and Clifford parallel $(n-1)$-planes in $EL^{2n-1}$
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1. The $n$-planes in $E^{2n}$
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2. Condition for two $n$-planes in $E^{2n}$ to be isoclinic with each other
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3. Maximal sets of mutually isoclinic $n$-planes in $E^2n$ and of mutually Clifford-parallel ($n-1$)-planes in $EL^{2n-1}$. Existence of such maximal sets
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4. An application: $n$-dimensional $C^2$-surfaces in $E^{2n}$ with mutually isoclinic tangent $n$-planes
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5. Some properties of maximal sets
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6. Numbers of non-congruent maximal sets — proof of Theorem 3.4
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7. Further properties of maximal sets
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8. Maximal sets of mutually isoclinic $n$-planes in $E^{2n}$ as submanifolds of the Grassmann manifold $G(n,n)$ of $n$-planes in $E^{2n}$
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Part II. The Hurwitz matrix equations
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1. Historial remarks
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2. Some lemmas on matrices
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3. Reduction of real solutions to quasi-solutions
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4. Existence of real solutions — the Hurwitz-Radon theorem
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5. Construction and properties of the real solutions
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6. Further properties of the real solutions
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7. The maximal real solutions
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8. The cases $n = 2$, $4$, $8$
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
-
Chapters
-
Introduction
-
Part I. Isoclinic $n$-planes in $E^{2n}$ and Clifford parallel $(n-1)$-planes in $EL^{2n-1}$
-
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 Clifford-parallel ($n-1$)-planes in $EL^{2n-1}$. 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 non-congruent 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
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1. Historial remarks
-
2. Some lemmas on matrices
-
3. Reduction of real solutions to quasi-solutions
-
4. Existence of real solutions — the Hurwitz-Radon 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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