Araştırma Makalesi
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On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space

Yıl 2018, Cilt: 11 Sayı: 2, 104 - 110, 30.11.2018
https://doi.org/10.36890/iejg.545137

Öz

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.

Kaynakça

  • [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.
Yıl 2018, Cilt: 11 Sayı: 2, 104 - 110, 30.11.2018
https://doi.org/10.36890/iejg.545137

Öz

Kaynakça

  • [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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

İrina Kuzmina Bu kişi benim

Patrik Peška Bu kişi benim

Yayımlanma Tarihi 30 Kasım 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 11 Sayı: 2

Kaynak Göster

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. Kasım 2018;11(2):104-110. doi:10.36890/iejg.545137
Chicago Kuzmina, İrina, ve Patrik Peška. “On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space”. International Electronic Journal of Geometry 11, sy. 2 (Kasım 2018): 104-10. https://doi.org/10.36890/iejg.545137.
EndNote Kuzmina İ, Peška P (01 Kasım 2018) On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space. International Electronic Journal of Geometry 11 2 104–110.
IEEE İ. Kuzmina ve P. Peška, “On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space”, Int. Electron. J. Geom., c. 11, sy. 2, ss. 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 (Kasım 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 ve Patrik Peška. “On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space”. International Electronic Journal of Geometry, c. 11, sy. 2, 2018, ss. 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.