arXiv research

In this paper, we describe a new surprising example of a fibration of the Clifford torus S3 x S3 in the 7-sphere by great 3-spheres, which is fiberwise homogeneous but whose fibers are not parallel to one another. In particular it is not part of a Hopf fibration. A fibration is fiberwise homogeneous when for any two fi…

In the paper of Montgomery, D. and Yang, C.T. [5], they discuss the de-suspension of smooth free actions of S1 on (2n+1)-dimensional homotopy spheres. In this paper we discuss the de-suspension of smooth free actions of S3 on (4n + 3)-dimensional homotopy spheres.

Study of Dirac operators on S3 and S2 spheres.

A peculiarity of the geometry of the euclidean 3-sphere $\S3$ is that it allows for the existence of compact without boundary minimally immersed surfaces. Despite a wealthy of examples of such surfaces, the only known tori minimally embedded in $\S3$ are the ones congruent to the Clifford torus. In 1970 Lawson conjectu…

Minimal surfaces in S3(2) linked to vector fields on punctured sphere.

A Smale flow is a structurally stable flow with one dimensional invariant sets. We use information from homology and template theory to construct, visualize and in some cases, classify, nonsingular Smale flows in the 3-sphere.

The aim of this paper is to present a complete description of all rotational linear Weingarten surface into the Euclidean sphere S3. These surfaces are characterized by a linear relation aH+bK=c, where H and K stand for their mean and Gaussian curvatures, respectively, whereas a; b and c are real constants.

New Lagrangian torus found in nearly Kaehler S3×S3.

Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes…

Study extends contact cosmetic surgeries to non-trivial Legendrian knots in L-spaces.

given two minimal surfaces embedded in $\S3$ of genus $g$ we prove the existence of a sequence of non-congruent compact minimal surfaces embedded in $\S3$ of genus $g$ that converges in $C^{2,α}$ to a compact embedded minimal surface provided some conditions are satisfied. These conditions also imply that, if any of th…

We provide a characterization of the Clifford Torus in S3 via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S3 with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

In this paper, we define a certain "proportional volume property" for an unit vector field on a spherical domain in S3. We prove that the volume of these vector fields has an absolute minimum and this value is equal to the volume of the Hopf vector field. Some examples of such vector fields are given. We also study the…

Special shadow-complexity equals k+1 for k copies of S1×S3.

Let k be a knot in S3. In [8], H.N. Howards and J. Schultens introduced a method to construct a manifold decomposition of double branched cover of (S3, k) from a thin position of k. In this article, we will prove that if a thin position of k induces a thin decomposition of double branched cover of (S3,k) by Howards and…

We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting properties: it is subadditive under connected sum and finite-to-one on …

Study on triaxial Bianchi IX metrics and Ricci flow singularity.

In this paper are given examples of tori T^2 embedded in S^3 with all their asymptotic lines dense.

Study proves existence of MOTTs in de Sitter spacetime.

In this paper are given examples of tori T2 embedded in R3 with all their principal lines dense. These examples are obtained by stereographic projection of deformations of the Clifford torus in S3.

DAHA and skein algebra on a double-torus knot are studied.

Study defines and proves Hard Lefschetz Property for S^3-actions.

Cannon and Swenson have shown that each hyperbolic 3-manifold group has a natural subdivision rule on the space at infinity, and that this subdivision rule captures the action of the group on the sphere. Explicit subdivision rules have also been found for some closed and finite-volume hyperbolic manifolds, as well as a…

In earlier work, carrying out numerical simulations of the Ricci flow of families of rotationally symmetric geometries on $S3$, we have found strong support for the contention that (at least in the rotationally symmetric case) the Ricci flow for a ``critical'' initial geometry - one which is at the transition point bet…

Explains minimal surfaces and their properties.

No characterizing slopes for multi-component links.

Study shows torsion order bounds band-unlinking number for knot cobordisms.

This is a survey on the global theory of constant mean curvature surfaces in Riemannian homogeneous 3-manifolds. These ambient 3-manifolds include the eight canonical Thurston 3-dimensional geometries, i.e. R3, H3, S3, H2 \times R, S2 \times R, the Heisenberg space Nil3, the universal cover of PSL2(R) and the Lie group…

Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal surfaces in the Euclidean spacce was presented in \cite{s3}. We…

Computes upper bounds for instanton knot homology.

A surgery formula for a specific 4-manifold invariant.

The WRT invariant of a link L in S2xS1 at sufficiently high values of the level r can be expresses as an evaluation of a special polynomial invariant of L at 2r-th root of unity. We categorify this polynomial invariant by associating to L a bigraded homology whose graded Euler characteristic is equal to this polynomial…

The aim of this paper is to expose some geometrical properties of the locally Minkowski-Cartan space with the Berwald-Moor metric of momenta. This space is regarded as a particular case of the $m$-th root Cartan space. Thus, Section 2 studies the $v$-covariant derivation components of the $m$-th root Cartan space. Sect…

We study sequences $f_k:Σ_k \to \R^n$ of conformally immersed, compact Riemann surfaces with fixed genus and Willmore energy ${\cal W}(f) \leq Λ$. Assume that $Σ_k$ converges to $Σ$ in moduli space, i.e. $φ_k^\ast(Σ_k) \to Σ$ as complex structures for diffeomorphisms $φ_k$. Then we construct a branched conformal immers…

The paper studies reducibility properties in Sasakian geometry, classifying certain contact structures and extremal metrics.

The study proves knots and certain links support taut foliations.

Specialized knot theory theorems for strongly involutive links.

Novel analysis of generalized Ricci solitons leads to stability results and deformations.

Topological field theories of 2- and 3-forms in 6D, showing no propagating degrees of freedom.

A flat complex vector bundle (E,D) on a compact Riemannian manifold (X,g) is stable (resp. polystable) in the sense of Corlette [C] if it has no D-invariant subbundle (resp. if it is the D-invariant direct sum of stable subbundles). It has been shown in [C] that the polystability of (E,D) in this sense is equivalent to…

Deep model forecasts correlated multivariate time series.

The paper extends Lie superalgebras of type D(2,1;a) to singular values.

Paper develops large time series models using pre-trained transformers.

New research finds 145 infinite families of CS spheres are standard.

Every smooth 4-sphere is the same as the standard one.

Paper shows maps from m-sphere to n-sphere are trivial cobordant.

The study classifies branched Willmore spheres in 3- and 4-spheres.

Kervaire's sphere-link is equivalent to a ribbon sphere-link, simplifying complex 2-complexes.