Cover Image

On the existence of vector fields with a given set of singular points on a two-dimensional closed oriented manifold

We study the possibility of constructing locally gradient and arbitrary vector fields with a given set of singular points on a two-dimensional closed oriented manifold. The sum of the indices of the vector field at these points is equal to the Euler characteristic of the manifold.

Saved in:

Bibliographic Details
Date:	1993
Main Authors:	Girik, E. A., Гирик, Е. А.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 1993
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/5980
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Vector fields with a given set of singular points
by: Prishlyak, O. O., et al.
Published: (1997)

Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds
by: Işim Efe, M., et al.
Published: (2017)

Necessary and sufficient condition for the existence of the one-point time on an oriented set
by: Ya. I. Hrushka
Published: (2019)

О существовании на двумерном замкнутом ориентируемом многообразии векторных полей с заданным набором особых точек
by: Гирик, Е.А.
Published: (1993)

Distinguishing graph of function with three critical points on a closed 3-manifold
by: Prishlyak, O., et al.
Published: (2025)

Functions and Vector Fields on C(CPⁿ)-Singular Manifolds
by: A. K.M. Libardi, et al.
Published: (2014)

On the construction of a set of stochastic differential equations on the basis of a given integral manifold independent of velocities
by: Azhymbaev, D. T., et al.
Published: (2010)

Functions and Vector Fields on $C(ℂP^N)$-Singular Manifolds
by: Libardi, Alice Kimie Miwa, et al.
Published: (2014)

Relative Chebyshev point of a system of continuously varying bounded closed sets
by: Hnatyuk, Yu. V., et al.
Published: (2011)

Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold
by: Hladysh, B.I., et al.
Published: (2017)

Realization of a closed 1-form on closed oriented surfaces
by: Budnyts'ka, N. V., et al.
Published: (2012)

Admissible vector fields and related diffusions on infinite-dimensional manifolds
by: Elworthy, K.D., et al.
Published: (1997)

Admissible vector fields and related diffusions on infinite-dimensional manifolds
by: Elworthy, K. D., et al.
Published: (1997)

The Plasticity of Some Fittable Surfaces on a Given Quadruple of Points in the Three-Dimensional Euclidean Space
by: A. N. Zachos
Published: (2014)

Quantum Modularity for a Closed Hyperbolic 3-Manifold
by: Wheeler, Campbell
Published: (2025)

Sets of independent vectors in spaces of unlimitedly growing dimensionality
by: Stepakhno , V. I., et al.
Published: (1992)

Sets of singular points of actions of finite groups by $(S^n)^k$
by: Plakhta , L. P., et al.
Published: (1992)

On the existence of a generalized asymmetric (α, β)-spline whose average values have equal minima at given points
by: Skorokhodov, D. S., et al.
Published: (2009)

Singularities of Toric Manifolds
by: Obikhod, T. V., et al.
Published: (2001)

Elliptic systems in extended Sobolev scale on a closed manifold
by: T. N. Zinchenko
Published: (2014)

Conditions for the existence of solutions of real nonautonomous systems of quasilinear differential equations vanishing at a singular point
by: Evtukhov, V. M., et al.
Published: (2010)

Optimal search for two active balls on a given set
by: G. A. Donets, et al.
Published: (2015)

Existence of Pareto-optimal solutions to the vector optimization problem with an unbounded feasible set
by: T. I. Serhiienko
Published: (2015)

On the existence of a surface in the pseudo-Euclidean space with given Grassman image
by: M. A. Grechneva, et al.
Published: (2016)

On the existence of a surface in the pseudo-Euclidean space with given Grassman image
by: Grechneva, M. A., et al.
Published: (2016)

On properties of central manifolds of a stationary point
by: Lykova, O. B., et al.
Published: (1997)

Elliptic pseudodifferential operators in the improved scale of spaces on a closed manifold
by: Murach, A. A., et al.
Published: (2007)

Symmetries of a center singularity of a plane vector fields
by: Maksymenko, S.I.
Published: (2009)

Topological Equivalence of Morse–Smale Vector Fields with beh2 on Three-Dimensional Manifolds
by: Prishlyak, O. O., et al.
Published: (2002)

A criterion for Banach manifolds to be finite-dimensional
by: Savkin, V. I., et al.
Published: (1995)

On the existence of a measurable function with given values of the best approximations in $L_0$
by: Pichugov, S. A., et al.
Published: (1996)

On the existence of a cyclic vector of some families of operators
by: Lytvynov, E. V.
Published: (1993)

On the existence of a cyclic vector for some families of operators
by: Lytvynov, E. V., et al.
Published: (1993)

The challenge in understanding the best balanced distance from a point to a set of uniform recovery of functional dependence, given inaccurate by a multi-valued mapping
by: U. V. Hudyma, et al.
Published: (2015)

An unsupervised, iterative N-dimensional point-set registration algorithm
by: P. Hosseinbor, et al.
Published: (2022)

An unsupervised, iterative $N$-dimensional point-set registration algorithm
by: Hosseinbor, P., et al.
Published: (2022)

Singular Reduction of Generalized Complex Manifolds
by: Goldberg, T.E.
Published: (2010)

Some results of searching three or four active balls on a given set
by: H. P. Donets, et al.
Published: (2017)

Generalized (CO)Homology length of a Manifold and functions with Singular Submanifolds
by: Bondar', O. P., et al.
Published: (1996)

Full measure of a set of singular continuous measures
by: Koshmanenko, V. D., et al.
Published: (2009)