The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions

Irina A. Kuzmina; Josef Mikeš; Alena Vanžurová

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2011)

  • Volume: 50, Issue: 1, page 91-98
  • ISSN: 0231-9721

Abstract

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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.

How to cite

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Kuzmina, Irina A., Mikeš, Josef, and Vanžurová, Alena. "The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 50.1 (2011): 91-98. <http://eudml.org/doc/196927>.

@article{Kuzmina2011,
abstract = {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.},
author = {Kuzmina, Irina A., Mikeš, Josef, Vanžurová, Alena},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {conformal mapping; geodesic mapping; conformal-geodesic mapping; initial conditions; (pseudo-) Riemannian space; conformal mapping; geodesic mapping; conformal-geodesic mapping; initial conditions; (pseudo-) Riemannian space},
language = {eng},
number = {1},
pages = {91-98},
publisher = {Palacký University Olomouc},
title = {The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions},
url = {http://eudml.org/doc/196927},
volume = {50},
year = {2011},
}

TY - JOUR
AU - Kuzmina, Irina A.
AU - Mikeš, Josef
AU - Vanžurová, Alena
TI - The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2011
PB - Palacký University Olomouc
VL - 50
IS - 1
SP - 91
EP - 98
AB - 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.
LA - eng
KW - conformal mapping; geodesic mapping; conformal-geodesic mapping; initial conditions; (pseudo-) Riemannian space; conformal mapping; geodesic mapping; conformal-geodesic mapping; initial conditions; (pseudo-) Riemannian space
UR - http://eudml.org/doc/196927
ER -

References

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  1. Berger, M., Geometry I, Springer, New York– Berlin–Heidelberg, 1987. (1987) Zbl0606.51001
  2. Jukl, M., On homologies of Klingenberg projective spaces oven special commutative local rings, Publ. Math. Univ. Debrec. 55 (1999), 113–121. (1999) MR1708406
  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. (2009) Zbl1202.51005MR2558710
  4. Kuzmina, I. A., Shapukov, B. N., Conformal and elliptic models of the Hopf fibration, Tr. geom. sem. Kazan. Univ. 24 (2003), 81–98. (2003) 
  5. Luonesto, P., Clifford Algebras and Spinors, Cambridge Univ. Press, Cambridge, 1997. (1997) MR1473721
  6. Norden, A. P., Normalization theory and vector bundles, Tr. Geom. Semin. 9 (1976), 68–76, (in Russian). (1976) Zbl0466.53006MR0493799
  7. Norden, A. P., Spaces of Affine Connection, Nauka, Moscow, 1976. (1976) MR0467565
  8. Rozenfeld, B. A., Higher-dimensional Spaces, Nauka, Moscow, 1966. (1966) 
  9. Rozenfeld, B. A., Geometry of Lie Groups, Kluwer, Dordrecht–Boston–London, 1997. (1997) 
  10. Shapukov, B. N., Connections on a differential fibred bundle, Tr. geom. sem. Kazan. Univ. 1 (1980), 97–109. (1980) 
  11. Shirokov, A. P., Non-Euclidean Spaces, Kazan University, Kazan, 1997, (in Russian). (1997) Zbl0933.51011

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