Related papers: Why cigar can not be isometrically immersed into t…
We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 1+3 covariant and 1+3 orthonormal frame notation, and show there exists a series of constraint equations that…
We consider the decay of cosmic strings that are trapped in the false vacuum in a theory of scalar electrodynamics in 3+1 dimensions. We restrict our analysis to the case of thin-walled cosmic strings which occur when large magnetic flux…
We study the topologically twisted cigar, namely the SL(2,R)/U(1) superconformal field theory at arbitrary level, and find the BRST cohomology of the topologically twisted N=2 theory. We find a one to one correspondence between the spectrum…
In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3d) form. Motivated by earlier studies of dark-bright solitons in the 1d case, we explore the stability of these structures in their…
In the theory of minimal submanifold, the following problem is fundamental: when does a given Riemannian manifold admit (or does not admit) a minimal isometric immersion into an Euclidean space form of arbitrary dimension? A partial…
Let the warped product $M^n=L^m\times_\varphi F^{n-m}$, $n\geq m+3\geq 8$, of Riemannian manifolds be an Einstein manifold with Ricci curvature $\rho$ that admits an isometric immersion into Euclidean space with codimension two. Under the…
A well-known result asserts that any isometric immersion with flat normal bundle of a Riemannian manifold with constant sectional curvature into a space form is (at least locally) holonomic. In this note, we show that this conclusion…
Oscillons are long-lived, slowly radiating solutions of nonlinear classical relativistic field theories. Recently it was discovered that in one spatial dimension their decay may proceed in "staccato" bursts. Here we perform a systematic…
We present exact numerical solutions in the form of spatially localized three-dimensional (3D) nonrotating and rotating (azimuthon) multipole solitons in the Bose-Einstein condensate (BEC) confined by a parabolic trap. We numerically show…
We report results of a systematic analysis of matter-wave gap solitons (GSs) in three-dimensional self-repulsive Bose-Einstein condensates (BECs) loaded into a combination of a cigar-shaped trap and axial optical-lattice (OL) potential.…
We study the non Ricci flat gradient steady K\"{a}hler Ricci soliton with non-negative Ricci curvature and weak integrability condition of the scalar curvature $S$, namely $\underline{\lim}_{r\to \infty} r^{-1}\int_{B_r} S=0$, and show that…
We investigate the dynamics of a Bose-Einstein condensate in a progressively bended three dimensional cigar shaped potential. The interplay between geometry and nonlinearity is considered. At high curvature, topological localization occurs…
We prove the existence of $C^{1,1}$ isometric immersions of several classes of metrics on surfaces $(\mathcal{M},g)$ into the three-dimensional Euclidean space $\mathbb{R}^3$, where the metrics $g$ have strictly negative curvature. These…
We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy.…
We prove the following statement: Let g be a light-line-complete pseudo-Riemannian Einstein metric of indefinite signature on a connected (n>2)-dimensional manifold M. Assume that a conformally equivalent metric is also Einstein. Then, the…
We present several local and global results on isometric immersions of Kaehler manifolds $M^{2n}$ into hyperbolic space $\Hy^{2n+p}$. For instance, a classification is given in the case of dimension $n\geq 4$ and codimension $p=2$.…
We study the old problem of isometrically embedding a 2-dimensional Riemannian manifold into Euclidean 3-space. It is shown that if the Gaussian curvature vanishes to finite order and its zero set consists of two Lipschitz curves…
We derive and analyze exact static solutions to the gravitating O(3) $\sigma$ model with cosmological constant in (2+1) dimensions. Both signs of the gravitational and cosmological constants are considered. Our solutions include…
A manifold is T-embedded into an affine space if its tangent spaces at distinct points are disjoint. We prove that an n-dimensional disc cannot be T-embedded into 2n-dimensional space.
We construct three-dimensional N=1 QED with N_f flavors using branes of type IIB string theory. This theory has a mirror, which can be realized using the S-dual brane configuration. As in examples with more supersymmetry, the Higgs branch…