TY  - BOOK
AU  - Wong,Yung-chow
TI  - Isoclinic n-planes in Euclidean 2n-space, Clifford parallels in elliptic (2n-1)-space, and the Hurwitz matrix equations
T2  - Memoirs of the American Mathematical Society, 
SN  - 9780821899854 (online)
AV  - QA3 .A57 no. 41
PY  - 1961///
CY  - Providence, R.I.
PB  - American Mathematical Society
KW  - Geometry, Analytic
KW  - Functional analysis
N1  - Includes bibliographical references; 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; 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 $n = 2$, $4$, $8$; Access is restricted to licensed institutions; Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2012
UR  - https://www-ams-org.libraryproxy.ist.ac.at/books/memo/0041
ER  -