Isoclinic n-planes in Euclidean 2n-space, Clifford parallels in elliptic (2n-1)-space, and the Hurwitz matrix equations / [electronic resource] by Yung-chow Wong.
Material type: TextSeries: Memoirs of the American Mathematical Society ; no. 41.Publication details: Providence, R.I. : American Mathematical Society, 1961Description: 1 online resource (112 p.)ISBN: 9780821899854 (online)Subject(s): Geometry, Analytic | Functional analysisAdditional physical formats: Isoclinic n-planes in Euclidean 2n-space, Clifford parallels in elliptic (2n-1)-space, and the Hurwitz matrix equations /LOC classification: QA3 | .A57 no. 41Online resources: Contents | ContentsCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK12494 |
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 $n = 2$, $4$, $8$
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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012
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