Regularities of the theory of quasi-geodesic mappings of special parabolic spaces
We study quasi-geodesic mappings (QGM) of generalized-recurrent-parabolic spaces f: (Vn, gij, Fih) → (V'n, g'ij, Fih). QGM can be of two types: general and canonical. This article examines the QGM of the general type. Earlier, we considered the fundamental questions of the theory of QGM of...
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| Language: | English |
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Odesa National University of Technology
2024-12-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
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| Online Access: | https://journals.ontu.edu.ua/index.php/geometry/article/view/2781 |
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| author | Iryna Kurbatova Nadiia Konovenko Margaret Pistruil |
| author_facet | Iryna Kurbatova Nadiia Konovenko Margaret Pistruil |
| author_sort | Iryna Kurbatova |
| collection | DOAJ |
| description | We study quasi-geodesic mappings (QGM) of generalized-recurrent-parabolic spaces f: (Vn, gij, Fih) → (V'n, g'ij, Fih). QGM can be of two types: general and canonical. This article examines the QGM of the general type. Earlier, we considered the fundamental questions of the theory of QGM of generalized-recurrent-parabolic spaces. We proved theorems that allow for any generalized-recurrent-parabolic space (Vn, gij, Fih) to either find all spaces (V'n, g'_{ij}, Fih) on which Vn admits QGM of the general form, or prove that there are no such spaces.
In this article, we constructed a Γ-transformation that makes it possible to obtain from a pair of generalized-recurrent-parabolic spaces that are in a quasi-geodesic mapping, an infinite sequence of pairs of other generalized-recurrent-parabolic spaces, which are also in a quasi-geodesic mapping. |
| format | Article |
| id | doaj-art-47962f26b23c45abbacffa19532e1a54 |
| institution | Kabale University |
| issn | 2072-9812 2409-8906 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj-art-47962f26b23c45abbacffa19532e1a542025-01-14T08:44:23ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062024-12-0117325627110.15673/pigc.v17i3.27812781Regularities of the theory of quasi-geodesic mappings of special parabolic spacesIryna KurbatovaNadiia KonovenkoMargaret PistruilWe study quasi-geodesic mappings (QGM) of generalized-recurrent-parabolic spaces f: (Vn, gij, Fih) → (V'n, g'ij, Fih). QGM can be of two types: general and canonical. This article examines the QGM of the general type. Earlier, we considered the fundamental questions of the theory of QGM of generalized-recurrent-parabolic spaces. We proved theorems that allow for any generalized-recurrent-parabolic space (Vn, gij, Fih) to either find all spaces (V'n, g'_{ij}, Fih) on which Vn admits QGM of the general form, or prove that there are no such spaces. In this article, we constructed a Γ-transformation that makes it possible to obtain from a pair of generalized-recurrent-parabolic spaces that are in a quasi-geodesic mapping, an infinite sequence of pairs of other generalized-recurrent-parabolic spaces, which are also in a quasi-geodesic mapping.https://journals.ontu.edu.ua/index.php/geometry/article/view/2781affine structurequasi-geodesic mappingpseudo-riemannian space |
| spellingShingle | Iryna Kurbatova Nadiia Konovenko Margaret Pistruil Regularities of the theory of quasi-geodesic mappings of special parabolic spaces Pracì Mìžnarodnogo Geometričnogo Centru affine structure quasi-geodesic mapping pseudo-riemannian space |
| title | Regularities of the theory of quasi-geodesic mappings of special parabolic spaces |
| title_full | Regularities of the theory of quasi-geodesic mappings of special parabolic spaces |
| title_fullStr | Regularities of the theory of quasi-geodesic mappings of special parabolic spaces |
| title_full_unstemmed | Regularities of the theory of quasi-geodesic mappings of special parabolic spaces |
| title_short | Regularities of the theory of quasi-geodesic mappings of special parabolic spaces |
| title_sort | regularities of the theory of quasi geodesic mappings of special parabolic spaces |
| topic | affine structure quasi-geodesic mapping pseudo-riemannian space |
| url | https://journals.ontu.edu.ua/index.php/geometry/article/view/2781 |
| work_keys_str_mv | AT irynakurbatova regularitiesofthetheoryofquasigeodesicmappingsofspecialparabolicspaces AT nadiiakonovenko regularitiesofthetheoryofquasigeodesicmappingsofspecialparabolicspaces AT margaretpistruil regularitiesofthetheoryofquasigeodesicmappingsofspecialparabolicspaces |