Application of Computer Mathematics Systems for Solving Problems of Contact Geometry
- Authors: Slavolyubova Y.V.1
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Affiliations:
- T.F. Gorbachev Kuzbass State Technical University
- Issue: Vol 9, No 3 (2022)
- Pages: 37-44
- Section: Articles
- URL: https://journals.eco-vector.com/2313-223X/article/view/529857
- DOI: https://doi.org/10.33693/2313-223X-2022-9-3-37-44
- ID: 529857
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Abstract
Task. The development of research in the field of contact geometry is impossible without the use of computer mathematics systems. Carrying out a computational experiment allows not only obtaining numerical results, analytical expressions, but also highlighting the correct and promising direction in obtaining theoretical results. Purpose of the work: to consider the application of computer mathematics systems to solving problems of contact geometry. Achieving the goals set in the work is carried out on the basis of the integrated use of computer algebra methods, mathematical modeling, the theory of differential geometry and tensor analysis. Findings. In this paper, we present schemes for studying contact Lie groups of arbitrary odd dimension. An algorithm and a set of programs have been developed in the Maxima computer mathematics system for modeling the proof of the existence of Sasakian structures. Practical value. This algorithm can be used to study contact structures on homogeneous spaces. The proposed schemes are of scientific and practical interest for specialists in the field of differential geometry and methods of its applications, as well as for solving the problems of developing quantum computing devices.
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About the authors
Yaroslavna Viktorovna Slavolyubova
T.F. Gorbachev Kuzbass State Technical University
Email: slavolubovayav@kuzstu.ru
Cand. Sci. (Phys.-Math.), Associate Professor; associate professor at the Department of Applied Information Technologies Kemerovo, Russian Federation
References
- Blair D.E. Riemannian geometry of contact and symplectic manifolds. In: Progress in Math. Birkhauser, 2010. 203 p.
- Becker T. Geodesic and conformally Reeb vector fields on flat 3-manifolds [Electronic resource]. URL: https://arxiv.org/abs/2207.03274 (data of accesses: 12.07.2022).
- Diatta A. Left invariant contact structures on Lie groups // Diff. Geom. аnd its Appl. Vol. 26. Iss. 5. Pp. 544-552. DOI: https://doi.org/10.1016/j.difgeo.2008.04.001.
- Marín-Salvador A. On the canonical contact structure of the space of null geodesics of a spacetime [Electronic resource]. URL: https://arxiv.org/abs/2109.03656 (data of accesses: 12.07.2022).
- Min H. The contact mapping class group and rational unknots in lens spaces [Electronic resource]. URL: https://arxiv.org/abs/2207.03590 (data of accesses: 12.07.2022).
- Dacko P. Rank of Jacobi operator and existence of quadratic parallel differential form, with applications to geometry of almost Para-contact metric manifolds [Electronic resource]. URL: https://arxiv.org/abs/1806.05604 (data of accesses: 12.07.2022).
- Dattin C. Sutured contact homology, conormal stops and hyperbolic knots [Electronic resource]. URL: https://arxiv.org/abs/2206.07782 (data of accesses: 12.07.2022).
- Teruya M. Almost contact structures on the deformation space of rational curves in a 4-dimensional twistor space [Electronic resource]. URL: https://arxiv.org/abs/2206.13151 (data of accesses: 12.07.2022).
- Dyakonov V.P. New computer algebra systems MAXIMA and wxMAXIMA. Components and Technologies. 2014. No. 2. Pp. 117-126. (In Rus.)
- Kirenberg A.G., Slavolyubova Ya.V. Real and predictive assessment of the degree of influence of radio channel noise on the data transfer rate in Wi-Fi wireless networks. Comp. Nanotechnol. 2019. Vol. 6. No. 1. Pp. 53-59. (In Rus.)
- Slavolyubova Ya.V. Associated left-invariant contact metric structures on the 7-dimensional Heisenberg group H7. Tomsk State University. Journal of Mathematics and Mechanics. 2018. No. 54. Pp. 34-45. (In Rus.)
- Slavolyubova Y.V. Contact metric structures on odd-dimensional unit spheres. Tomsk State University. Journal of Mathematics and Mechanics. 2014. No. 6. Pp. 46-54. (In Rus.)
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