Праці міжнародного геометричного центру (Proceedings of the International Geometry Center)geom-center.ontu.edu.uahttps://card-file.ontu.edu.ua/handle/123456789/61922024-11-03T16:31:03Z2024-11-03T16:31:03Z1151Canonical quasi-geodesic mappings of special pseudo-Riemannian spacesIrina Kurbatova, M. Pistruilhttps://card-file.ontu.edu.ua/handle/123456789/250202023-05-10T13:25:22Z2022-01-01T00:00:00Zdc.title: Canonical quasi-geodesic mappings of special pseudo-Riemannian spaces
dc.contributor.author: Irina Kurbatova, M. Pistruil
dc.description.abstract: The present paper continues the study of quasi-geodesic mappings f:(Vn, gij, Fih) → (V'n,g'ij, Fih) of pseudo-Riemannian spaces Vn, V'n with a generalized-recurrent structure Fih of parabolic type. By a generalized recurrent structure of parabolic type on Vn we mean an almost Hermitian affinor structure of parabolic type for which the covariant derivative of the structural affinor Fih satisfies the condition F(i,j)h=q(i Fj)h.
In the previous paper by the authors [Proc. Intern. Geom. Center, 13:3 (2020) 18-32] it was proved that the class of pseudo-Riemannian spaces with generalized-recurrent structure of parabolic type is closed with respect to the considered mappings and the generalized recurrence vectors in (Vn, gij,Fih) and (V'_n, g'ij, Fih) may be distinct. In this article, it is assumed that the mapping f preserves the generalized recurrence vector qi.
We construct geometric objects that are invariant under the quasi-geodesic mapping of generalized-recurrent spaces of parabolic type and recurrent-parabolic spaces. A number of conditions are given on these objects, which lead to the fact that a generalized-recurrent space of parabolic type admits a parabolic K-structure, and a recurrent-parabolic space admits a Kählerian structure of parabolic type.
We study special types of these mappings that preserve some tensors of an intrinsic nature.
2022-01-01T00:00:00ZExplicit formulae for Chern-Simons invariants of the hyperbolic J(2n,-2m) knot orbifoldsJi-Young Ham, Joongul Leehttps://card-file.ontu.edu.ua/handle/123456789/250162023-05-10T13:25:22Z2023-01-01T00:00:00Zdc.title: Explicit formulae for Chern-Simons invariants of the hyperbolic J(2n,-2m) knot orbifolds
dc.contributor.author: Ji-Young Ham, Joongul Lee
dc.description.abstract: We calculate the Chern-Simons invariants of the hyperbolic double twist knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of cone-manifold structures of double twist knots.
2023-01-01T00:00:00ZSome remarks on a theorem of GreenAbdessami Ben Hmida Jalled, Fathi Hagguihttps://card-file.ontu.edu.ua/handle/123456789/250182023-05-10T13:25:22Z2022-01-01T00:00:00Zdc.title: Some remarks on a theorem of Green
dc.contributor.author: Abdessami Ben Hmida Jalled, Fathi Haggui
dc.description.abstract: The purpose of this paper is to study holomorphic curves f from C to C3 avoiding four complex hyperplanes and a real subspace of real dimension four in C3. We show that the projection of f into the complex projective space C P^2 does not remain constant as in the complex case studied by Green, which indicates that the complex structure of the avoided hyperplanes is a necessary condition in the Green theorem
2022-01-01T00:00:00ZOn geodesic mappings of symmetric pairsVolodymyr Kiosak, Olexandr Lesechko, Olexandr Latyshhttps://card-file.ontu.edu.ua/handle/123456789/250172023-05-10T13:25:22Z2023-01-01T00:00:00Zdc.title: On geodesic mappings of symmetric pairs
dc.contributor.author: Volodymyr Kiosak, Olexandr Lesechko, Olexandr Latysh
dc.description.abstract: The paper treats properties of pseudo-Riemannian spaces admitting non-trivial geodesic mappings. A symmetric pair of pseudo-Riemannian spaces is a pair of spaces with coinciding values of covariant derivatives for their Riemann tensors. It is proved that the symmetric pair of pseudo-Riemannian spaces, which are not spaces of constant curvatures, are defined unequivocally by their geodesic lines. The research is carried out locally, using tensors, with no restrictions to the sign of the metric tensor and the signature of a space.
2023-01-01T00:00:00ZQuasiconformal mappings and curvatures on metric measure spacesJialong Denghttps://card-file.ontu.edu.ua/handle/123456789/250152023-05-10T13:25:22Z2023-01-01T00:00:00Zdc.title: Quasiconformal mappings and curvatures on metric measure spaces
dc.contributor.author: Jialong Deng
dc.description.abstract: In an attempt to develop higher-dimensional quasiconformal mappings on metric measure spaces with curvature conditions, i.e. from Ahlfors to Alexandrov, we show that for n≥2 a noncollapsed RCD(0,n) space with Euclidean volume growth is an n-Loewner space and satisfies the infinitesimal-to-global principle.
2023-01-01T00:00:00ZTopological structure of optimal flows on the Girl's surfaceAlexandr Prishlyak, Maria Losevahttps://card-file.ontu.edu.ua/handle/123456789/250192023-05-10T13:25:22Z2023-01-01T00:00:00Zdc.title: Topological structure of optimal flows on the Girl's surface
dc.contributor.author: Alexandr Prishlyak, Maria Loseva
dc.description.abstract: We investigate the topological structure of flows on the Girl's surface which is one of two possible immersions of the projective plane in three-dimensional space with one triple point of self-intersection. First, we describe the cellular structure of the Boy's and Girl's surfaces and prove that there are unique images of the project plane in the form of a $2$-disk, in which the opposite points of the boundary are identified and this boundary belongs to the preimage of the $1$-skeleton of the surface. Second, we describe three structures of flows with one fixed point and no separatrices on the Girl's surface and prove that there are no other such flows. Third, we prove that Morse-Smale flows and they alone are structurally stable on the Boy's and Girl's surfaces. Fourth, we find all possible structures of optimal Morse-Smale flows on the Girl's surface. Fifth, we obtain a classification of Morse-Smale flows on the projective plane immersed on the Girl's surface. And finally, we describe the isotopic classes of these flows.
2023-01-01T00:00:00ZMonogenic functions and harmonic vectorsSergiy Plaksahttps://card-file.ontu.edu.ua/handle/123456789/250112023-05-10T13:23:46Z2023-01-01T00:00:00Zdc.title: Monogenic functions and harmonic vectors
dc.contributor.author: Sergiy Plaksa
dc.description.abstract: We consider special topological vector spaces with a commutative multiplication for some of elements of the spaces and monogenic functions taking values in these spaces.Monogenic functions are understood as continuous and differentiable in the sense of G^ateaux functions.We describe relations between the mentioned monogenic functions and harmonic vectors in the three-dimensional real space and establish sufficient conditions for infinite monogeneity of functions. Unlike the classical complex analysis, it is done in the case where the validity of the Cauchy integral formula for monogenic functions remains an open problem.
2023-01-01T00:00:00Zσ-monogenic functions in commutative algebrasVitalii Shpakivskyihttps://card-file.ontu.edu.ua/handle/123456789/250102023-05-10T13:23:46Z2023-01-01T00:00:00Zdc.title: σ-monogenic functions in commutative algebras
dc.contributor.author: Vitalii Shpakivskyi
dc.description.abstract: In finite-dimensional commutative associative algebra, the concept of σ-monogenic function is introduced. Necessary and sufficient conditions for σ-monogeneity have been established. In some low-dimensional algebras, with a special choice of σ, the representation of σ-monogenic functions is obtained using holomorphic functions of a complex variable. We proposed the application of σ-monogenic functions with values in two-dimensional biharmonic algebra to representation of solutions of two-dimensional biharmonic equation.
2023-01-01T00:00:00ZA.K. Bakhtin. Scientific legacyIryna Denega, Yaroslav Zabolotnyihttps://card-file.ontu.edu.ua/handle/123456789/250142023-05-10T13:23:46Z2023-01-01T00:00:00Zdc.title: A.K. Bakhtin. Scientific legacy
dc.contributor.author: Iryna Denega, Yaroslav Zabolotnyi
dc.description.abstract: In the paper we give a brief overview of the O. Bakhtin' scientific results
2023-01-01T00:00:00ZOn weakly 1-convex sets in the planeТетяна Осіпчук, Максим Володимирович Ткачукhttps://card-file.ontu.edu.ua/handle/123456789/250132023-05-10T13:23:46Z2023-01-01T00:00:00Zdc.title: On weakly 1-convex sets in the plane
dc.contributor.author: Тетяна Осіпчук, Максим Володимирович Ткачук
dc.description.abstract: The present work considers the properties of generally convex sets in the plane known as weakly 1-convex. An open set is called weakly 1-convex if for any boundary point of the set there exists a straight line passing through this point and not intersecting the given set. A closed set is called weakly 1-convex if it is approximated from the outside by a family of open weakly 1-convex sets. A point of the complement of a set to the whole plane is called a 1-nonconvexity point of the set if any straight passing through the point intersects the set. It is proved that if an open, weakly 1-convex set has a non-empty set of 1-nonconvexity points, then the latter set is also open. It is also shown that the non-empty interior of a closed, weakly 1-convex set in the plane is weakly 1-convex.
2023-01-01T00:00:00Z