On the Geometric Singularities of Surfaces of Pseudo-Euclidean Space

Year 2018, , 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.