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
https://doi.org/10.36890/iejg.545137

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.

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
https://doi.org/10.36890/iejg.545137

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 This is me

Patrik Peška This is me

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.