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.

By: Wong, Yung-chowMaterial type: TextTextSeries: 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 | Contents
Contents:
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 $n = 2$, $4$, $8$
Item type: E-BOOKS
Tags from this library: No tags from this library for this title. Log in to add tags.
    Average rating: 0.0 (0 votes)
Current library Home library Call number Materials specified URL Status Date due Barcode
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 $n = 2$, $4$, $8$

Access is restricted to licensed institutions

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Mode of access : World Wide Web

Description based on print version record.

There are no comments on this title.

to post a comment.
The Institute of Mathematical Sciences, Chennai, India

Powered by Koha