Research Article
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On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space

Year 2018, Volume: 11 Issue: 2, 104 - 110, 30.11.2018

İrina Kuzmina Patrik Peška

https://doi.org/10.36890/iejg.545137
Cited By: 1

Abstract

In this article we explore the space of constant curvature. We consider the principal bundle over
pseudoconformal plane. The elements of differential geometry are found for a surface of pseudo-
Euclidean space. The elements of the matrix of the metric tensor, as well as the coefficients of the
Riemannian connection, are calculated.

Keywords

principal bundle space of constant curvature pseudo-Euclidean space Riemannian connection

References

  • [1] Belova N.E. Bundles of 4th dimensional algebras. Kazan: Kazan University, 1999. 44 p. Dep. in VINITI 11.10.99, No. 3037-B99.
  • [2] Kotelnikov A.P. Screw calculus and some applications of it to geometry and mechanics. Kazan, 1895.
  • [3] Kuzmina I.A., Shapukov B.N. Conformal and elliptic models of the Hopf fibration. Tr. geom. sem. Kazan: Kazan University, 2003. Issue 24. 81-98.
  • [4] Kuzmina I.A., Mikeš J. On pseudoconformal models of fibrations determined by the algebra of antiquaternions and projectivization of them. Annales Mathematicae et Informaticae, 2013. 42. 57-64.
  • [5] Mikeš J. et al., Differential geometry of special mappings, Palacky Univ. Press, Olomouc, 2015.
  • [6] Rozenfeld B.A. Higher-dimensional spaces. Moscow: Nauka, 1966. 647 p.
  • [7] Shapukov B.N. Connections on a differential fibred bundle. Tr. geom. sem. Kazan: Kazan University, 1980. Issue 12. 97-109.
  • [8] Shirokov A.P. Geometry of tangent bundles and spaces over algebras. The results of science and technology. Ser. Probl. geom., VINITI, M., 1981. 12. 6195.
  • [9] Shirokov A.P. Geometry of generalized biaxial spaces. Scien. Univ. app. Kazan, 1954. 114:2. 123166.
  • [10] Shirokov A.P. The space H4 and the quaternion algebra. Tr. geom. sem. Kazan: Kazan University, 1997. Issue 23. 187198.
  • [11] Shirokov P.A. Constant fields of second-order vectors and tensors in Riemannian spaces. Izv. fiz.-mat. Soc. KSU, 1925. ser. 2, t. 25. 86-114.
  • [12] Shirokov P.A. On one type of symmetric spaces. Selected works on geometry. Kazan, 1966. 408-418.
  • [13] Shirokov P.A. On an application of a screw calculus to differential geometry. Selected works on geometry. Kazan, 1966. 315-318.
  • [14] Vishnevsky V.V. Polynomial algebras and affinor structures. Tr. geom. sem. Kazan: Kazan University, 1971. Issue 6. 2235.
  • [15] Vishnevsky V.V., Shirokov A.P., Shurygin V.V. Spaces over Algebras. Kazan University Press, 1985. 262 p.
  • [16] Zeiliger D.N. Complex line geometry. L.-M. Gostekhizdat, 1934.

Year 2018, Volume: 11 Issue: 2, 104 - 110, 30.11.2018

İrina Kuzmina Patrik Peška

https://doi.org/10.36890/iejg.545137
Cited By: 1

Abstract

References

  • [1] Belova N.E. Bundles of 4th dimensional algebras. Kazan: Kazan University, 1999. 44 p. Dep. in VINITI 11.10.99, No. 3037-B99.
  • [2] Kotelnikov A.P. Screw calculus and some applications of it to geometry and mechanics. Kazan, 1895.
  • [3] Kuzmina I.A., Shapukov B.N. Conformal and elliptic models of the Hopf fibration. Tr. geom. sem. Kazan: Kazan University, 2003. Issue 24. 81-98.
  • [4] Kuzmina I.A., Mikeš J. On pseudoconformal models of fibrations determined by the algebra of antiquaternions and projectivization of them. Annales Mathematicae et Informaticae, 2013. 42. 57-64.
  • [5] Mikeš J. et al., Differential geometry of special mappings, Palacky Univ. Press, Olomouc, 2015.
  • [6] Rozenfeld B.A. Higher-dimensional spaces. Moscow: Nauka, 1966. 647 p.
  • [7] Shapukov B.N. Connections on a differential fibred bundle. Tr. geom. sem. Kazan: Kazan University, 1980. Issue 12. 97-109.
  • [8] Shirokov A.P. Geometry of tangent bundles and spaces over algebras. The results of science and technology. Ser. Probl. geom., VINITI, M., 1981. 12. 6195.
  • [9] Shirokov A.P. Geometry of generalized biaxial spaces. Scien. Univ. app. Kazan, 1954. 114:2. 123166.
  • [10] Shirokov A.P. The space H4 and the quaternion algebra. Tr. geom. sem. Kazan: Kazan University, 1997. Issue 23. 187198.
  • [11] Shirokov P.A. Constant fields of second-order vectors and tensors in Riemannian spaces. Izv. fiz.-mat. Soc. KSU, 1925. ser. 2, t. 25. 86-114.
  • [12] Shirokov P.A. On one type of symmetric spaces. Selected works on geometry. Kazan, 1966. 408-418.
  • [13] Shirokov P.A. On an application of a screw calculus to differential geometry. Selected works on geometry. Kazan, 1966. 315-318.
  • [14] Vishnevsky V.V. Polynomial algebras and affinor structures. Tr. geom. sem. Kazan: Kazan University, 1971. Issue 6. 2235.
  • [15] Vishnevsky V.V., Shirokov A.P., Shurygin V.V. Spaces over Algebras. Kazan University Press, 1985. 262 p.
  • [16] Zeiliger D.N. Complex line geometry. L.-M. Gostekhizdat, 1934.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

İrina Kuzmina

Patrik Peška

Publication Date November 30, 2018
Published in Issue Year 2018 Volume: 11 Issue: 2

Cite

APA Kuzmina, İ., & Peška, P. (2018). On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space. International Electronic Journal of Geometry, 11(2), 104-110. https://doi.org/10.36890/iejg.545137
AMA Kuzmina İ, Peška P. On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space. Int. Electron. J. Geom. November 2018;11(2):104-110. doi:10.36890/iejg.545137
Chicago Kuzmina, İrina, and Patrik Peška. “On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space”. International Electronic Journal of Geometry 11, no. 2 (November 2018): 104-10. https://doi.org/10.36890/iejg.545137.
EndNote Kuzmina İ, Peška P (November 1, 2018) On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space. International Electronic Journal of Geometry 11 2 104–110.
IEEE İ. Kuzmina and P. Peška, “On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space”, Int. Electron. J. Geom., vol. 11, no. 2, pp. 104–110, 2018, doi: 10.36890/iejg.545137.
ISNAD Kuzmina, İrina - Peška, Patrik. “On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space”. International Electronic Journal of Geometry 11/2 (November 2018), 104-110. https://doi.org/10.36890/iejg.545137.
JAMA Kuzmina İ, Peška P. On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space. Int. Electron. J. Geom. 2018;11:104–110.
MLA Kuzmina, İrina and Patrik Peška. “On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space”. International Electronic Journal of Geometry, vol. 11, no. 2, 2018, pp. 104-10, doi:10.36890/iejg.545137.
Vancouver Kuzmina İ, Peška P. On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space. Int. Electron. J. Geom. 2018;11(2):104-10.

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