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Isoclinic $n$-planes in Euclidean $2n$-space, Clifford parallels in elliptic $(2n-1)$-space, and the Hurwitz matrix equations
About this Title
Yung-chow Wong
Publication: Memoirs of the American Mathematical Society
Publication Year:
1961; Number 41
ISBNs: 978-0-8218-1241-9 (print); 978-0-8218-9985-4 (online)
DOI: https://doi.org/10.1090/memo/0041
MathSciNet review: 0145437
Table of Contents
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 โ proof of Theoremย 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 quasi-solutions
- 4. Existence of real solutions โ 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 $n = 2$, $4$, $8$