Isoclinic N-Planes in Euclidean 2n-Space, Clifford Parallels in Elliptic(2n-1) Space and the Hurwitz Matrix Equations.
Wong, Yung-Chow.
Isoclinic N-Planes in Euclidean 2n-Space, Clifford Parallels in Elliptic(2n-1) Space and the Hurwitz Matrix Equations. - 1st ed. - 1 online resource (121 pages) - Memoirs of the American Mathematical Society ; v.1 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Introduction -- Part I. Isoclinic n-planes in E[sup(2n)] and Clifford-parallel (n-l)-planes in EL[sup(2n-1)] -- 1. The n-planes in E[sup(2n)] -- 2. Condition for two n-planes in E[sup(2n)] to be isoclinico -- 3. Maximal sets of mutually isoclinic n-planes in E[sup(2n)] and of mutually Clifford-parallel (n-l)-planes in EL[sup(2n-1)] . Existence of such maximal sets -- 4. An application: n-dimensional C[sup(2)]-surfaces in E[sup(2n)] whose tangent n-planes are mutually isoclinic -- 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[sup(2n)] as submanifolds of the Grassmann manifold G(n,n) of n-planes in E[sup(2n)] -- Part II. The Hurwitz matrix equations -- 1. Historial remarks -- 2. Some lemmas on matrices -- 3. Reduction of the 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 -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- M -- O -- Q -- R -- S -- U.
9780821899854
Geometry, Analytic.
Electronic books.
QA551.W66 1961
Isoclinic N-Planes in Euclidean 2n-Space, Clifford Parallels in Elliptic(2n-1) Space and the Hurwitz Matrix Equations. - 1st ed. - 1 online resource (121 pages) - Memoirs of the American Mathematical Society ; v.1 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Introduction -- Part I. Isoclinic n-planes in E[sup(2n)] and Clifford-parallel (n-l)-planes in EL[sup(2n-1)] -- 1. The n-planes in E[sup(2n)] -- 2. Condition for two n-planes in E[sup(2n)] to be isoclinico -- 3. Maximal sets of mutually isoclinic n-planes in E[sup(2n)] and of mutually Clifford-parallel (n-l)-planes in EL[sup(2n-1)] . Existence of such maximal sets -- 4. An application: n-dimensional C[sup(2)]-surfaces in E[sup(2n)] whose tangent n-planes are mutually isoclinic -- 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[sup(2n)] as submanifolds of the Grassmann manifold G(n,n) of n-planes in E[sup(2n)] -- Part II. The Hurwitz matrix equations -- 1. Historial remarks -- 2. Some lemmas on matrices -- 3. Reduction of the 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 -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- M -- O -- Q -- R -- S -- U.
9780821899854
Geometry, Analytic.
Electronic books.
QA551.W66 1961