Cover Image

On 2-dimensional surfaces in 3-dimensional and 4-dimensional Euclidean spaces. Results and unsolved problems

We present a survey of the results obtained for 2-dimensional surfaces in $E^3$ and $E^4$ and connected with the Gaussian curvature and Gaussian torsion. In this connection, we consider the Monge –Amp´ere equations, obtain the generalizations of Bernstein’s integral formula, and establish some lower...

Full description

Saved in:

Bibliographic Details
Date:	2019
Main Authors:	Aminov, Yu. A., Аминов, Ю. А.
Format:	Article
Language:	Russian
Published:	Institute of Mathematics, NAS of Ukraine 2019
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/1416
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

On 2-dimensional surfaces in 3-dimensional and 4-dimensional Euclidean spaces. Results and unsolved problems
by: Ju. A. Aminov
Published: (2019)

On Isometric Immersions of the Lobachevsky Plane into 4-Dimensional Euclidean Space with Flat Normal Connection
by: Y. Aminov
Published: (2020)

A study on tensor product surfaces in low-dimensional Euclidean spaces
by: Etemad, Dehkordy A., et al.
Published: (2012)

A study on tensor product surfaces in low-dimensional Euclidean spaces
by: Etemad Dehkordy, A.
Published: (2012)

On the geometric results of A. V. Pogorelov
by: Aminov, Yu. A., et al.
Published: (2007)

Solving the Hermite interpolation problem in a finite-dimensional Euclidean space
by: O. F. Kashpur
Published: (2022)

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

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

Biharmonic Hopf Hypersurfaces of Complex Euclidean Space and Odd Dimensional Sphere
by: N. Mosadegh, et al.
Published: (2020)

Generalized Elastic Line Deformed on a Nonnull Surface by an External Field in the 3-Dimensional Semi-Euclidean Space E₁³
by: Gürbüz, N., et al.
Published: (2015)

Generalized Elastic Line Deformed on Non-null Surface by an External Field in the 3-Dimensional Semi-Euclidean Space E31
by: N. Gьrbьz, et al.
Published: (2015)

Generalized Elastic Line Deformed on a Nonnull Surface by an External Field in the 3-Dimensional Semi-Euclidean Space $\mathbb{E}_1^3$
by: Gorgula, V. I., et al.
Published: (2015)

Compact Spacelike Surfaces in the 3-Dimensional de Sitter Space
by: Borisenko, A.A.
Published: (2006)

The emergence and formation of the theory of optimal set partitioning for sets of the n-dimensional Euclidean space. Theory and applications
by: E. M. Kiseleva
Published: (2018)

The Fourier sums: new results and unsolved problems
by: Stepanets, A. I., et al.
Published: (1988)

On Isometric Immersion of Three-Dimensional Geometries $SL_2$, $Nil$ and $Sol$ into a Four-Dimensional Space of Constant Curvature
by: Masal'tsev, L. A., et al.
Published: (2005)

Leiko Network on the Surfaces in the Euclidean Space E3
by: I. V. Potapenko
Published: (2015)

Leiko Network on the Surfaces in the Euclidean Space $E_3$
by: Potapenko, I. V., et al.
Published: (2015)

Cauchy problem for the essentially infinite-dimensional heat equation on a surface in a Hilbert space
by: Bogdanskii, Yu. V., et al.
Published: (1995)

Nonlinear Transformations of Smooth Measures on Infinite-Dimensional Spaces
by: Kulik, A. M., et al.
Published: (2000)

Infinite Dimensional Spaces and Cartesian Closedness
by: P. Giordano
Published: (2011)

Infinite Dimensional Spaces and Cartesian Closedness
by: Giordano, P.
Published: (2011)

Fredholm one-dimensional boundary-value problems in Sobolev spaces
by: Atlasiuk, O. M., et al.
Published: (2018)

Cauchy problem for the essentially infinite-dimensional heat equation on a surface in a Hilbert space
by: Bogdansky, Yu.V.
Published: (1995)

Fredholm one-dimensional boundary-value problems in Sobolev spaces
by: O. M. Atlasiuk, et al.
Published: (2018)

Low-dimensional structures on the surface of indium phosphide
by: Ya. O. Sychikova
Published: (2012)

Invariants of Surfaces in Three-Dimensional Affine Geometry
by: Arnaldsson, Örn, et al.
Published: (2021)

Two-dimensional pseudospherical surfaces with degenerate Bianchi transformation
by: Gor'kavyi, V. A., et al.
Published: (2011)

Fredholm one-dimensional boundary-value problems with parameter in Sobolev spaces
by: Atlasiuk, O. M., et al.
Published: (2018)

Middle-sectioned simplices in a four-dimensional affine space
by: Reznikova, Yu. S., et al.
Published: (2007)

From one-dimensional to infinite-dimensional dynamical systems: Ideal turbulence
by: Romanenko, O. Yu., et al.
Published: (1996)

Quasi-Bi-Hamiltonian Structures of the 2-Dimensional Kepler Problem
by: Cariñena, J.F., et al.
Published: (2016)

О геометрических работах А. В. Погорелова
by: Аминов, Ю.А.
Published: (2007)

Решение проблемы построения подмногообразия по заданному грассманову образу
by: Аминов, Ю.А.
Published: (2010)

Fredholm one-dimensional boundary-value problems with parameter in Sobolev spaces
by: O. M. Atlasiuk, et al.
Published: (2018)

Second order nonlinear Cauchy problems in a four dimensional space
by: Di Bartolomeo, A., et al.
Published: (2003)

On the one-dimensional two-phase inverse Stefan problems
by: Zhernovoi, Yu. V., et al.
Published: (1993)

Reduction of three-dimensional theory of thick plates bending to solving two two-dimensional problems
by: V. P. Revenko
Published: (2015)

On differentiability of mappings of finite-dimensional domains into Banach spaces
by: Bondar, A. V., et al.
Published: (1999)

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