Sobolev Institute of Mathematics

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19932026

most citedPhysics Interplay of the LHC and the ILC

408 citations

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math.DG2024

Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates

Victor Alexandrov

The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a linear differential equation of the first order, which previous…

math.DG2023

On the formality problem for manifolds with special holonomy

Iskander A. Taimanov

In sections 1 and 2 we follow our online talk at the 21st Geometrical Seminar (Beograd, Serbia) on June 30, 2022 by giving a survey of the formality problem for manifold with speci…

math.DG2022★ 3 cited

Surfaces via spinors and soliton equations

Iskander A. Taimanov

This article surveys the Weierstrass representation of surfaces in the three- and four-dimensional spaces, with an emphasis on its relation to the Willmore functional. We also desc…

math.DG2022★ 9 cited

Trace formula for the magnetic Laplacian on a compact hyperbolic surface

Yuri A. Kordyukov, Iskander A. Taimanov

We compute the trace formula for the magnetic Laplacian on a compact hyperbolic surface of constant curvature with constant magnetic field for energies above the Mane critical leve…

math.DG2021★ 1 cited

A note on the first-order flexes of smooth surfaces which are tangent to the set of all nonrigid surfaces

Victor Alexandrov

We prove that first-order flexes of smooth surfaces in Euclidean 3-space, which are tangent to the set of all nonrigid surfaces, can be extended to second-order flexes.

math.DG2020★ 8 cited

The second closed geodesic, the fundamental group, and generic Finsler metrics

Hans-Bert Rademacher, Iskander A. Taimanov

For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics.…

math.DG2020

Around Efimov's differential test for homeomorphism

Victor Alexandrov

In 1968, N.\,V.~Efimov proved the following remarkable theorem: \textit{Let $f : R^{2} \to R^{2} \in C^{1}$ be such that $det f^{'} (x) < 0$ for all $x \in R^{2}$ and let th…

math.DG2019★ 13 cited

Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class

Yaroslav V. Bazaikin, Anton S. Galaev, Pavel Gumenyuk

The paper deals with a modified Godbillon-Vey class defined by Losik for codimension-one foliations. This characteristic class takes values in the cohomology of the second order fr…

math.DG2019

On Hamiltonian minimality of isotropic non-homogeneous tori in $H^{n}$ and $C P^{2 n + 1}$

Mikhail Ovcharenko

We construct a family of flat isotropic non-homogeneous tori in $H^{n}$ and $C P^{2 n + 1}$ and find necessary and sufficient conditions for their Hamiltonian…

math.DG2019★ 15 cited

Trace formula for the magnetic Laplacian

Yuri A. Kordyukov, Iskander A. Taimanov

The Guillemin-Uribe trace formula is a semiclassical version of the Selberg trace formula and more general Duistermaat-Guillemin formula for elliptic operators on compact manifolds…

math.DG2018★ 13 cited

Losik classes for codimension-one foliations

Yaroslav V. Bazaikin, Anton S. Galaev

Following Losik's approach to Gelfand's formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Suff…

math.DG2018★ 4 cited

Closed geodesics on connected sums and 3-manifolds

Hans-Bert Rademacher, Iskander A. Taimanov

We study the asymptotics of the number N(t) of geometrically distinct closed geodesics of a Riemannian or Finsler metric on a connected sum of two compact manifolds of dimension at…

math.DG2018★ 6 cited

On homogeneous geodesics and weakly symmetric spaces

V. N. Berestovskii, Yu. G. Nikonorov

In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an $1$ -parameter isometry group. As an application of…

math.DG2016

The spectrum of the Laplace operator on connected compact simple rank four Lie groups. I

Irina Zubareva

In this paper are given explicit calculations of Laplace operator spectrum for smooth real/complex-valued functions on all connected compact simple rank four Lie groups with biinva…

math.DG2015

The spectrum of the Laplace operator on connected compact simple rank three Lie groups

Valera Berestovskii, Irina Zubareva, Victor Svirkin

In this paper are given explicit calculations of Laplace operator spectrum for smooth real/complex-valued functions on all connected compact simple rank three Lie groups with biinv…

math.DG2015

Geodesics and shortest arcs of special sub-Riemannian metric on the Lie group $S L (2)$

V. Berestovskii, I. Zubareva

The authors found geodesics, shortest arcs, cut loci, and conjugate sets for left-invariant sub-Riemannian matric on the Lie group $S L (2)$ , which is right-invariant relative to the…

math.DG2015★ 1 cited

Sub-Riemannian distance on the Lie group $S O_{0} (2, 1)$

V. Berestovskii, I. Zubareva

A left-invariant sub-Riemannian metric $d$ on the shortened Lorentz group $S O_{0} (2, 1)$ under the condition that $d$ is right-invariant relative to the orthogonal Lie subgroup $1\oti…

math.DG2015★ 59 cited

Sub-Riemannian curvature in contact geometry

Andrei Agrachev, Davide Barilari, Luca Rizzi

We compare different notions of curvature on contact sub-Riemannian manifolds. In particular we introduce canonical curvatures as the coefficients of the sub-Riemannian Jacobi equa…

math.DG2014

Locally compact homogeneous spaces with inner metric

V. N. Berestovskii

The author reviews his results on locally compact homogeneous spaces with inner metric, in particular, homogeneous manifolds with inner metric. The latter are isometric to homogene…

math.DG2014

On a new incomplete Ricci-flat metric

Evgeny Malkovich

We define a system of ODE that gives Einstein 4-dimensional metrics. We found new Ricci-flat incomplete metric of cohomogeneity 1 in explicit formulas and study its characteristics…

math.DG2014

The Moutard transformation of two-dimensional Dirac operators and the Mobius geometry

Iskander A. Taimanov

We describe the action of the (Mobius) inversion on the data of the Weierstrass representation of surfaces in the three-space and show that the Moutard transformation of two-dimens…

math.DG2013★ 5 cited

Hamiltonian minimal Lagrangian submanifolds in toric varieties

Andrey Mironov, Taras Panov

Hamiltonian minimality (H-minimality) for Lagrangian submanifolds is a symplectic analogue of Riemannian minimality. A Lagrangian submanifold is called H-minimal if the variations…

math.DG2012

Spectral curves for Cauchy-Riemann operators on punctured elliptic curves

Christoph Bohle, Iskander A. Taimanov

We show that one can define a spectral curve for the Cauchy-Riemann operator on a punctured elliptic curve if one imposes appropriate boundary conditions. Algebraic curves of the t…

math.DG2012★ 15 cited

Generalized normal homogeneous Riemannian metrics on spheres and projective spaces

V. N. Berestovskii, Yu. G. Nikonorov

In this paper we develop new methods of study of generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homog…

Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates

On the formality problem for manifolds with special holonomy

Surfaces via spinors and soliton equations

Trace formula for the magnetic Laplacian on a compact hyperbolic surface

A note on the first-order flexes of smooth surfaces which are tangent to the set of all nonrigid surfaces

The second closed geodesic, the fundamental group, and generic Finsler metrics

Around Efimov's differential test for homeomorphism

Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class

On Hamiltonian minimality of isotropic non-homogeneous tori in Hn and CP2n+1

Trace formula for the magnetic Laplacian

Losik classes for codimension-one foliations

Closed geodesics on connected sums and 3-manifolds

On homogeneous geodesics and weakly symmetric spaces

The spectrum of the Laplace operator on connected compact simple rank four Lie groups. I

The spectrum of the Laplace operator on connected compact simple rank three Lie groups

Geodesics and shortest arcs of special sub-Riemannian metric on the Lie group SL(2)

Sub-Riemannian distance on the Lie group SO0​(2,1)

Sub-Riemannian curvature in contact geometry

Locally compact homogeneous spaces with inner metric

On a new incomplete Ricci-flat metric

The Moutard transformation of two-dimensional Dirac operators and the Mobius geometry

Hamiltonian minimal Lagrangian submanifolds in toric varieties

Spectral curves for Cauchy-Riemann operators on punctured elliptic curves

Generalized normal homogeneous Riemannian metrics on spheres and projective spaces

On Hamiltonian minimality of isotropic non-homogeneous tori in $H^{n}$ and $C P^{2 n + 1}$

Geodesics and shortest arcs of special sub-Riemannian metric on the Lie group $S L (2)$

Sub-Riemannian distance on the Lie group $S O_{0} (2, 1)$