| Title:
|
The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions (English) |
| Author:
|
Kuzmina, Irina A. |
| Author:
|
Mikeš, Josef |
| Author:
|
Vanžurová, Alena |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
91-98 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Our aim is to study the principal bundles determined by the algebra of quaternions in the projective model. The projectivization of the conformal model of the Hopf fibration is considered as example. (English) |
| Keyword:
|
conformal mapping |
| Keyword:
|
geodesic mapping |
| Keyword:
|
conformal-geodesic mapping |
| Keyword:
|
initial conditions |
| Keyword:
|
(pseudo-) Riemannian space |
| MSC:
|
53B20 |
| MSC:
|
53B30 |
| MSC:
|
53C21 |
| idZBL:
|
Zbl 1252.53023 |
| idMR:
|
MR2920701 |
| . |
| Date available:
|
2011-12-08T09:52:02Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141722 |
| . |
| Reference:
|
[1] Berger, M.: Geometry I. Springer, New York– Berlin–Heidelberg, 1987. Zbl 0606.51001 |
| Reference:
|
[2] Jukl, M.: On homologies of Klingenberg projective spaces oven special commutative local rings. Publ. Math. Univ. Debrec. 55 (1999), 113–121. MR 1708406 |
| Reference:
|
[3] Jukl, M., Snášel, V.: Projective equivalence of quadrics in Klingenberg projective spaces over a special local ring. Int. Electr. J. Geom. 2 (2009), 34–38. Zbl 1202.51005, MR 2558710 |
| Reference:
|
[4] Kuzmina, I. A., Shapukov, B. N.: Conformal and elliptic models of the Hopf fibration. Tr. geom. sem. Kazan. Univ. 24 (2003), 81–98. |
| Reference:
|
[5] Luonesto, P.: Clifford Algebras and Spinors. Cambridge Univ. Press, Cambridge, 1997. MR 1473721 |
| Reference:
|
[6] Norden, A. P.: Normalization theory and vector bundles. Tr. Geom. Semin. 9 (1976), 68–76, (in Russian). Zbl 0466.53006, MR 0493799 |
| Reference:
|
[7] Norden, A. P.: Spaces of Affine Connection. Nauka, Moscow, 1976. MR 0467565 |
| Reference:
|
[8] Rozenfeld, B. A.: Higher-dimensional Spaces. Nauka, Moscow, 1966. |
| Reference:
|
[9] Rozenfeld, B. A.: Geometry of Lie Groups. Kluwer, Dordrecht–Boston–London, 1997. |
| Reference:
|
[10] Shapukov, B. N.: Connections on a differential fibred bundle. Tr. geom. sem. Kazan. Univ. 1 (1980), 97–109. |
| Reference:
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[11] Shirokov, A. P.: Non-Euclidean Spaces. Kazan University, Kazan, 1997, (in Russian). Zbl 0933.51011 |
| . |
