A Vector Field in a Semi-Riemannian Manifold
A Vector Field in a Semi-Riemannian Manifold
DOI:
https://doi.org/10.56143/ujmcs.v1i1.1Ключевые слова:
manifold; foliation;semi-Riemannian manifold; Minkowski space; spacelike; timelike; vector field.Аннотация
The study of vector fields in semi-Riemannian manifolds forms a critical component in differential geometry and mathematical physics. Semi-Riemannian manifolds generalize the concept of Riemannian manifolds by allowing the metric tensor to have indefinite signature, thus encompassing both Riemannian and Lorentzian manifolds. This generalization is essential for understanding the geometry underlying General Relativity and various field theories.
Библиографические ссылки
[1] Chen, B. Y.: Pseudo-Riemannian Geometry, delta-invariants and Applications. World Scientific Publishing, Hackensack, NJI(2011).
[2] Duggal, Krishan L., Sahin, B.: Differential geometry of lightlike submanifolds. Frontiers in Mathematics. Birkhäuser Verlag, Basel (2010).
[3] Fujioka, A., Furuhata, H., Sasaki, T.: Projective surfaces and pre-normalized Blaschke immersions of codimension two. Int. Electron. J. Geom. 9 (1), 100-110 (2016).
[4] Ilarslan, K.: New results for general helix in Euclidean 3-space. In: Proceedings of the 6th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA), Aug 15-18/2017, Budapest, HUNGARY. AIP Conference Proceedings. 1926, 1-6 (2018).
[5] O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press. London (1983).
[6] Özgür, C.: On C-Parallel Legendre Curves in Non-Sasakian Contact Metric Manifolds. Preprint arxiv:1906.03313 (2019).
[7] Sharipov, A. S., Topvoldiyev, F. F.: On invariant of surfaces with isometric on section. Mathematics and Statistics, 10(3), 523–528.
doi:10.13189/ms.2022.100307, (2022).
[8] Ismoilov, S. S., Sultanov, B. M.: Invariant geometric characteristics under the dual mapping of an isotropic space. Asia Pacific Journal of Mathematics, 10, 1–12. doi:10.28924/APJM/10-20, (2023).
[9] Ismoilov, S. S.: Geometry of the Monge - Ampere equation in an isotropic space. Uzbek Mathematical Journal, 66(2), 66–77, (2022).
[10] Artykbaev, A., Sultanov, B. M.: Invariants of surface indicatrix in a Special linear transformation. Mathematics and Statistics, 7(4), 106–115, (2019).
[11] Artykbaev, A., Ismoilov, S. S.: The dual surfaces of an isotropic space $R_{3}^{2} . Bulletin of the Institute of Mathematics, 4(4), 1–8, (2021).
[12] Artikbaev, A., Ismoilov, S. S.: Special mean and total curvature of a dual surface in isotropic spaces. International Electronic Journal of Geometry, 15(1), 1–10, (2022).
[13] Artikbayev, A., Ismoilov, S. S.: Surface recovering by a given total and mean curvature in isotropic space. Palestine Journal of Mathematics, 11(3), 351–361, (2022).
[14] O’Neill, B.: Semi-Riemannian Geometry With Applications to Relativity. Academic Press, (1983).
[15] Hawking, S. W., Ellis, G. F. R.: The Large Scale Structure of Space-Time.(1973).
[16] Matsumoto, M.: Semi-Riemannian Geometry. Saitama Mathematical Journal, 7, 8–22, (1989).
[17] Moser, J.: Duality in semi-Riemannian geometry. Communications in Mathematical Physics, 32(1), 37–52, (1973).
[18] Dubrovin, B. A., Fomenko, A. T., Novikov, S. P.: Modern Geometry—Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and Fields. Springer, (1984).
[19] Arnold, V. I.: Legendre Transformations in Contact Geometry. Proceedings of the International Congress of Mathematicians, 1, 391–404,(1990).
[20] Boyer, C.: Semi-Riemannian Geometry and General Relativity. Elsevier.(2017).
[21] Kupershmidt, B. A.:Geometry of jet bundles and the integrable systems. Springer Science, Business Media.(2002).
[22] Esposito, G.: Duality transformations in field theory and statistical mechanics. International Journal of Modern Physics A, 19(01), 135–146,(2004).
[23] Carroll, S. M.: Spacetime and Geometry: An Introduction to General Relativity,(2004).
[24] García-Río, E., Kupeli, D. N.: Semi-Riemannian Manifolds. In Semi-Riemannian Maps and Their Applications. Dordrecht: Springer
Netherlands,pp. 19–57,(1999).
[25] Gao, T., Lim, L.-H., Ye, K.: Semi-Riemannian Manifold Optimization. Journal of Geometry, 35(2). doi:10.1007/s00022-020-00500-1, (2018).
[26] Shahi, F.: Semi-Riemannian Structures on Manifolds. Journal of Differential Geometry, 112(2), 345–367, (2024).
[27] Smith, John.: Minimal Pseudo-Riemannian Submanifolds. Journal of Geometry, vol. 35, no. 2, Springer, pp. 123–145, (2020), https://doi.org/10.1007/s00022-020-00500-1.
